<?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>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>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>48321</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.77</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8734815</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-09-12</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="F3"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.77</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8708136</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F8"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-09-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5933</value>
                    <footnoteId id="F4"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.23</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8702203</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F7"/>
                    <footnoteId id="F10"/>
                    <footnoteId id="F11"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common stock, par value $0.01 per share</value>
            </securityTitle>
            <transactionDate>
                <value>2016-09-13</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="F6"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.23</value>
                    <footnoteId id="F5"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8698928</value>
                    <footnoteId id="F9"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnotes</value>
                    <footnoteId id="F8"/>
                    <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 as follows: (i) 9,095 shares by Waud Capital Partners II, L.P. (&quot;WCP II&quot;), (ii) 27,464 shares by Waud Capital Partners QP II, L.P. (&quot;Waud QP II&quot;), (iii) 5,811 shares by WCP FIF II (Acadia), L.P. (&quot;WCP FIF II&quot;) and (iv) 5,951 shares by Waud Capital Affiliates II, L.L.C. (&quot;Waud Affiliates II&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 Footnotes (1) and (3) to this Form 4.</footnote>
        <footnote id="F3">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="F4">Represents shares sold in multiple transactions under Rule 144 as follows: (i) 1,117 shares by WCP II, (ii) 3,372 shares by Waud QP II, (iii) 713 shares by WCP FIF II and (iv) 731 shares by Waud Affiliates II.</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 Footnotes (4) and (6) to this Form 4.</footnote>
        <footnote id="F6">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="F7">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.</footnote>
        <footnote id="F8">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="F9">The shares are owned of record as follows: (i) 1,297,373 shares by WCP II, (ii) 2,557,606 shares by WCP QP II, (iii) 751,113 shares by the Halcyon Exempt Family Trust (the &quot;Halcyon Trust&quot;), (iv) 83,530 shares by Waud Family Partners, L.P. (&quot;WFP LP&quot;), (v) 418,098 shares by WCP FIF II, (vi) 428,204 shares by Waud Affiliates II, (vii) 219,756 shares by Waud Affiliates III, (viii) 596,913 shares by WCP FIF III, (ix) 1,287,433 shares by WCP QP III, (x) 194,606 shares by WCP III, (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="F10">Mr. Waud may be deemed to beneficially own the shares of common stock described in Footnote (9) 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, (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>2016-09-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
