<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>2105100 - Disclosure - Other Comprehensive Income of the Operating Partnership</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2013Q2YTD</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000921112</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>3</Level><ElementName>lry_OtherComprehensiveIncomeLineItems</ElementName><ElementPrefix>lry_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Other Comprehensive Income [Line Items]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>us-gaap_ComprehensiveIncomeNoteTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-family:Times New Roman;font-size:10pt;"&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;text-decoration:underline;"&gt;Other Comprehensive Income (Loss) of the Trust&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The functional currency of the Trust's United Kingdom operations is pounds sterling.  The Trust translates the financial statements for the United Kingdom operations into US dollars.  Gains and losses resulting from this translation are included in accumulated other comprehensive income (loss) as a separate component of shareholders' equity.  A proportionate amount of gain or loss is allocated to noncontrolling interest - operating partnership - common units.  Accumulated other comprehensive income (loss) consists solely of the foreign currency translation adjustments described above.  Upon sale or upon complete or substantially complete liquidation of the Trust's foreign investment, the gain or loss on the sale will include the cumulative translation adjustments that have been previously recorded in accumulated other comprehensive income (loss) and noncontrolling interest - operating partnership - common units.  &lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for comprehensive income, which includes, but is not limited to, 1) the amount of income tax expense or benefit allocated to each component of other comprehensive income, including reclassification adjustments, 2) the reclassification adjustments for each classification of other comprehensive income and 3) the ending accumulated balances for each component of comprehensive income.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 130

 -Paragraph 14-26

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 14

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e681-108580



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 11

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e637-108580



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 505

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.3-04)

 -URI http://asc.fasb.org/extlink&amp;oid=6959260&amp;loc=d3e187085-122770



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 15

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e689-108580



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 1A

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=SL7669619-108580



Reference 7: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 17

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e716-108580



Reference 8: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 12

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e640-108580



Reference 9: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 16

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e709-108580



Reference 10: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Glossary Reclassification Adjustments

 -URI http://asc.fasb.org/extlink&amp;oid=6522872



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Comprehensive Income (Loss) Note [Text Block]</Label></Row><Row FlagID="0"><Id>3</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>0</Level><ElementName /><ElementPrefix /><IsBaseElement>true</IsBaseElement><BalanceType /><PeriodType /><IsReportTitle>false</IsReportTitle><IsSegmentTitle>true</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole /><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><OriginalInstanceReportColumn FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>true</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>D2013Q2YTD_dei_LegalEntityAxis_lry_LibertyPropertyLimitedPartnershipMember</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0000921112</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments><anyType xsi:type="Segment"><IsDefaultForEntity>false</IsDefaultForEntity><Name /><IsFromEntityGroup>false</IsFromEntityGroup><ValueName>Liberty Property Limited Partnership [Member]</ValueName><ValueType>dei_LegalEntityAxis</ValueType><Namespace>xbrldi</Namespace><Schema>http://xbrl.org/2006/xbrldi</Schema><DimensionInfo><Id>lry_LibertyPropertyLimitedPartnershipMember</Id><dimensionId>dei_LegalEntityAxis</dimensionId><type>explicitMember</type></DimensionInfo></anyType></Segments><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="dei_LegalEntityAxis:lry_LibertyPropertyLimitedPartnershipMember" Id="0" Label="Liberty Property Limited Partnership [Member]" /><Label Key="Calendar" Id="1" Label="1/1/2013 - 6/30/2013" /></Labels></OriginalInstanceReportColumn><ElementDataType>na</ElementDataType><SimpleDataType>na</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Liberty Property Limited Partnership [Member]</Label></Row><Row FlagID="0"><Id>4</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>3</Level><ElementName>lry_OtherComprehensiveIncomeLineItems</ElementName><ElementPrefix>lry_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Other Comprehensive Income [Line Items]</Label></Row><Row FlagID="0"><Id>5</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>4</Level><ElementName>us-gaap_ComprehensiveIncomeNoteTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="D2013Q2YTD_dei_LegalEntityAxis_lry_LibertyPropertyLimitedPartnershipMember" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div style="font-family:Times New Roman;font-size:10pt;"&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;font-weight:bold;text-decoration:underline;"&gt;Other Comprehensive Income (Loss) of the Operating Partnership&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;&lt;br clear="none"/&gt;&lt;/font&gt;&lt;/div&gt;&lt;div style="line-height:120%;text-align:justify;font-size:10pt;"&gt;&lt;font style="font-family:inherit;font-size:10pt;"&gt;The functional currency of the Operating Partnership&amp;#8217;s United Kingdom operations is pounds sterling. The Operating Partnership translates the financial statements for the United Kingdom operations into US dollars. Gains and losses resulting from this translation are included in general partner&amp;#8217;s equity and limited partners&amp;#8217; equity &amp;#8211; common units. Upon sale or upon complete or substantially complete liquidation of the Operating Partnership's foreign investment, the gain or loss on the sale will include the cumulative translation adjustments that have been previously recorded in general partner&amp;#8217;s equity and limited partners&amp;#8217; equity &amp;#8211; common units.&lt;/font&gt;&lt;/div&gt;&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for comprehensive income, which includes, but is not limited to, 1) the amount of income tax expense or benefit allocated to each component of other comprehensive income, including reclassification adjustments, 2) the reclassification adjustments for each classification of other comprehensive income and 3) the ending accumulated balances for each component of comprehensive income.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Statement of Financial Accounting Standard (FAS)

 -Number 130

 -Paragraph 14-26

 -LegacyDoc This reference is SUPERSEDED by the Accounting Standards Codification effective for interim and annual periods ending after September 15, 2009.  This reference is included to help users transition from the previous accounting hierarchy and will be removed from future versions of this taxonomy.



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 14

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e681-108580



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 11

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e637-108580



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 505

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.3-04)

 -URI http://asc.fasb.org/extlink&amp;oid=6959260&amp;loc=d3e187085-122770



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 15

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e689-108580



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 1A

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=SL7669619-108580



Reference 7: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 17

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e716-108580



Reference 8: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 12

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e640-108580



Reference 9: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 220

 -SubTopic 10

 -Section 45

 -Paragraph 16

 -URI http://asc.fasb.org/extlink&amp;oid=20435746&amp;loc=d3e709-108580



Reference 10: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Glossary Reclassification Adjustments

 -URI http://asc.fasb.org/extlink&amp;oid=6522872



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Comprehensive Income (Loss) Note [Text Block]</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Other Comprehensive Income of the Operating Partnership</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.libertyproperty.com/role/OtherComprehensiveIncomeOfOperatingPartnership</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>5</NumberOfRows></InstanceReport>
