<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2016-09-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001520697</issuerCik>
        <issuerName>Acadia Healthcare Company, Inc.</issuerName>
        <issuerTradingSymbol>ACHC</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001532461</rptOwnerCik>
            <rptOwnerName>WAUD CAPITAL PARTNERS III, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 N. LASALLE STREET, SUITE 4900</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001532462</rptOwnerCik>
            <rptOwnerName>WAUD CAPITAL PARTNERS MANAGEMENT III, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 N. LASALLE STREET, SUITE 4900</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001487016</rptOwnerCik>
            <rptOwnerName>WAUD CAPITAL PARTNERS III, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 N. LASALLE STREET, SUITE 4900</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001487019</rptOwnerCik>
            <rptOwnerName>WAUD CAPITAL PARTNERS QP III, L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 N. LASALLE STREET, SUITE 4900</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001532465</rptOwnerCik>
            <rptOwnerName>WCP FIF III (ACADIA), L.P.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 N. LASALLE STREET, SUITE 4900</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001532468</rptOwnerCik>
            <rptOwnerName>WAUD CAPITAL AFFILIATES III, L.L.C.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>300 N. LASALLE STREET, SUITE 4900</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-09-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>26679</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.77</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2301983</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-09-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>3275</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.23</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>2298708</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F3"/>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares sold in market transactions under Rule 144 as follows: (i) 665 shares by Waud Capital Partners III, L.P. (&quot;WCP III&quot;), (ii) 14,664 shares by Waud Capital Partners QP III, L.P. (&quot;Waud QP III&quot;), (iii) 8,296 shares by WCP FIF III (Acadia), L.P. (&quot;WCP FIF III&quot;)  and (iv) 3,054 shares by Waud Capital Affiliates III, L.L.C. (&quot;Waud Affiliates III&quot;).</footnote>
        <footnote id="F2">The price reported in Column 4 is a weighted average price. The shares were sold in multiple transactions under Rule 144 at prices ranging from $51.58 to $52.01, inclusive. The reporting persons undertake to provide to Acadia Healthcare Company, Inc., any security holder of Acadia Healthcare Company, Inc., or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in Footnote (1) to this Form 4.</footnote>
        <footnote id="F3">Reeve B. Waud is a member of the board of directors of Acadia Healthcare Company, Inc. Mr. Waud is also the manager of Waud Capital Partners III, L.L.C. (&quot;Waud III LLC&quot;) and a member of the Limited Partner Committee of Waud Capital Partners Management III, L.P. (&quot;WCPM III&quot;). Waud III LLC is the general partner of WCPM III. WCPM III is the general partner of WCP III, Waud QP III and WCP FIF III and the manager of Waud Affiliates III. As a result, each of Mr. Waud, Waud III LLC and WCPM III may be deemed to share beneficial ownership of the reported shares.</footnote>
        <footnote id="F4">Represents shares sold in market transactions under Rule 144 as follows: (i) 82 shares by WCP III, (ii) 1,800 shares by Waud QP III, (iii) 1,019 shares by WCP FIF III and (iv) 374 shares by Waud Affiliates III.</footnote>
        <footnote id="F5">The price reported in Column 4 is a weighted average price. The shares were sold in multiple transactions under Rule 144 at prices ranging from $51.15 to $51.85, inclusive. The reporting persons undertake to provide to Acadia Healthcare Company, Inc., any security holder of Acadia Healthcare Company, Inc., or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in Footnote (4) to this Form 4.</footnote>
        <footnote id="F6">The reported shares are owned of record as follows: (i) 194,606 shares by WCP III, (ii) 1,287,433 shares by Waud QP III, (iii) 596,913 shares by WCP FIF III and (iv) 219,756 shares by Waud Affiliates III.</footnote>
        <footnote id="F7">Each of the reporting persons expressly disclaims beneficial ownership of the reported shares except to the extent of its pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Waud Capital Partners III, L.L.C., by /s/ Reeve B. Waud, its manager</signatureName>
        <signatureDate>2016-09-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Waud Capital Partners Management III, L.P., by Waud Capital Partners III, L.L.C., its general partner, by /s/ Reeve B. Waud, its manager</signatureName>
        <signatureDate>2016-09-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Waud Capital Partners III, L.P., by Waud Capital Partners Management III, L.P., its general partner, by Waud Capital Partners III, L.L.C., its general partner, by /s/ Reeve B. Waud, its manager</signatureName>
        <signatureDate>2016-09-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Waud Capital Partners QP III, L.P., by Waud Capital Partners Management III, L.P., its general partner, by Waud Capital Partners III, L.L.C., its general partner, by /s/ Reeve B. Waud, its manager</signatureName>
        <signatureDate>2016-09-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>WCP FIF III (Acadia), L.P., by Waud Capital Partners Management III, L.P., its general partner, by Waud Capital Partners III, L.L.C., its general partner, by /s/ Reeve B. Waud, its manager</signatureName>
        <signatureDate>2016-09-14</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>Waud Capital Affiliates III, L.L.C., by Waud Capital Partners Management III, L.P., its manager, by Waud Capital Partners III, L.L.C., its general partner, by /s/ Reeve B. Waud, its manager</signatureName>
        <signatureDate>2016-09-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
