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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

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

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001421620</rptOwnerCik>
            <rptOwnerName>WAUD REEVE B</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O WAUD CAPITAL  PARTNERS, L.L.C.</rptOwnerStreet1>
            <rptOwnerStreet2>300 N. LASALLE STREET, SUITE 4900</rptOwnerStreet2>
            <rptOwnerCity>CHICAGO</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60654</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>14000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>35.79</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7323951</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F9"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>8841</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>34.86</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7315110</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F9"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5159</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>35.51</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7309951</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F9"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>13300</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.20</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7296651</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F9"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-12-14</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>700</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>33.88</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>7295951</value>
                    <footnoteId id="F8"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F9"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>55673</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares sold in multiple transactions under Rule 144 by the Halcyon Exempt Family Trust (the &quot;Halcyon Trust&quot;).</footnote>
        <footnote id="F2">The price reported in column 4 is a weighted average price. These shares were sold in multiple transactions under Rule 144 at prices ranging from $35.69 to $36.01, inclusive. The reporting person further undertakes to provide to Acadia Healthcare Company, Inc., any security holder of Acadia Healthcare Company, Inc., or the staff of the Securities and Exchange Commission (the &quot;Commission&quot;), upon request, full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F3">The price reported in column 4 is a weighted average price. These shares were sold in multiple transactions under Rule 144 at prices ranging from $34.31 to $35.305, inclusive. The reporting person further undertakes to provide to Acadia Healthcare Company, Inc., any security holder of Acadia Healthcare Company, Inc., or the staff of the Commission, upon request, full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F4">The price reported in column 4 is a weighted average price. These shares were sold in multiple transactions under Rule 144 at prices ranging from $35.31 to $35.97, inclusive. The reporting person further undertakes to provide to Acadia Healthcare Company, Inc., any security holder of Acadia Healthcare Company, Inc., or the staff of the Commission, upon request, full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F5">The price reported in column 4 is a weighted average price. These shares were sold in multiple transactions under Rule 144 at prices ranging from $32.68 to $33.67, inclusive. The reporting person further undertakes to provide to Acadia Healthcare Company, Inc., any security holder of Acadia Healthcare Company, Inc., or the staff of the Commission, upon request, full information regarding the number of shares sold at each separate price.</footnote>
        <footnote id="F6">The price reported in column 4 is a weighted average price. These shares were sold in multiple transactions under Rule 144 at prices ranging from $33.68 to $34.36, inclusive. The reporting person further undertakes to provide to Acadia Healthcare Company, Inc., any security holder of Acadia</footnote>
        <footnote id="F7">Mr. Waud is the investment advisor of the Halcyon Trust of which Mr. Waud's children are beneficiaries.</footnote>
        <footnote id="F8">The shares are owned of record as follows: (i) 1,141,420 shares by Waud Capital Partners II, L.P. (&quot;WCP II&quot;), (ii) 2,086,697 shares by Waud Capital Partners QP II, L.P. (&quot;WCP QP II&quot;), (iii) 634,113 shares by the Halcyon Trust, (iv) 83,530 shares by Waud Family Partners, L.P. (&quot;WFP LP&quot;), (v) 318,466 shares by WCP FIF II (Acadia), L.P. (&quot;WCP FIF II&quot;), (vi) 326,164 shares by Waud Capital Affiliates II, L.L.C. (&quot;Waud Affiliates II&quot;), (vii) 167,388 shares by Waud Capital Affiliates III, L.L.C. (&quot;Waud Affiliates III&quot;), (viii) 454,671 shares by WCP FIF III (Acadia), L.P. (&quot;WCP FIF III&quot;), (ix) 1,036,001 shares by Waud Capital Partners QP III, L.P. (&quot;WCP QP III&quot;), (x) 183,205 shares by Waud Capital Partners III, L.P. (&quot;WCP III&quot;), (xi) 33,333 shares by Melissa W. Waud, Mr. Waud's wife, (xii) 35,296 shares by Waud Capital Partners, L.L.C. (&quot;WCP LLC&quot;), and (xii) 795,667 shares by Crystal Cove LP.</footnote>
        <footnote id="F9">Waud Capital Partners Management II, L.P. (&quot;WCPM II&quot;) is the general partner of WCP II, WCP QP II and WCP FIF II and the manager of Waud Affiliates II. Waud Capital Partners II, L.L.C. (&quot;WCP II LLC&quot;) is the general partner of WCPM II. Waud Capital Partners Management III, L.P. (&quot;WCPM III&quot;) is the general partner of WCP FIF III, WCP QP III and WCP III and the manager of Waud Affiliates III. Waud Capital Partners III, L.L.C. (&quot;WCP III LLC&quot;) is the general partner of WCPM III.</footnote>
        <footnote id="F10">Mr. Waud may be deemed to beneficially own the shares of common stock reported herein by virtue of (A) his making decisions for the Limited Partner Committee of each of WCPM II and WCPM III, (B) his being the manager of WCP II LLC and WCP III LLC, (C) his being the general partner of WFP LP, (D) his being the investment advisor of the Halcyon Trust of which Mr. Waud's children are beneficiaries, (E) his being married to Ms. Waud, (F) his being the sole manager of WCP LLC and (G) his being the general partner of Crystal Cove LP.</footnote>
        <footnote id="F11">Mr. Waud expressly disclaims beneficial ownership of the reported shares except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Reeve B. Waud</signatureName>
        <signatureDate>2016-12-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
