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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-08-10</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001432313</rptOwnerCik>
            <rptOwnerName>Gordon Christopher R</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>C/O BAIN CAPITAL INVESTORS LLC</rptOwnerStreet1>
            <rptOwnerStreet2>JOHN HANCOCK TOWER, 200 CLARENDON ST.</rptOwnerStreet2>
            <rptOwnerCity>BOSTON</rptOwnerCity>
            <rptOwnerState>MA</rptOwnerState>
            <rptOwnerZipCode>02116</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</value>
            </securityTitle>
            <transactionDate>
                <value>2015-08-10</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>J</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
                <footnoteId id="F10"/>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>42778</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5803339</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                    <footnoteId id="F6"/>
                    <footnoteId id="F7"/>
                    <footnoteId id="F8"/>
                    <footnoteId id="F9"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1611</value>
                    <footnoteId id="F11"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Bain Capital Investors, LLC (&quot;BCI&quot;) is the general partner of Bain Capital Partners VIII, L.P. (&quot;BCP VIII&quot;), which is the general partner of Bain Capital Fund VIII, L.P., which is the sole member of Bain Capital Fund VIII, LLC (&quot;Fund VIII&quot;).</footnote>
        <footnote id="F2">BCI is the general partner of BCP VIII, which is the general partner of Bain Capital VIII Coinvestment Fund, L.P., which is the sole member of Bain Capital VIII Coinvestment Fund, LLC (&quot;Fund VIII-CO&quot;).</footnote>
        <footnote id="F3">BCI is also the general partner of Bain Capital (CR), L.P. (&quot;BC CR&quot;).</footnote>
        <footnote id="F4">BCI is also the managing partner of BCIP Associates III, which is the manager of BCIP Associates III, LLC (&quot;BCIP III&quot;).</footnote>
        <footnote id="F5">BCI is also the managing partner of BCIP Associates III-B, which is the manager of BCIP Associates III-B, LLC (&quot;BCIP III-B&quot;).</footnote>
        <footnote id="F6">BCI is also the managing partner of BCIP Trust Associates III, which is the manager of BCIP T Associates III, LLC (&quot;BCIPT III&quot;).</footnote>
        <footnote id="F7">BCI is also the managing partner of BCIP Trust Associates III-B, which is the manager of BCIP T Associates III-B, LLC (&quot;BCIPT III-B&quot;).</footnote>
        <footnote id="F8">BCI is also the managing partner of BCIP Associates-G (&quot;BCIP G&quot; and together with Fund VIII, Fund VIII-CO, BC CR, BCIP III, BCIP III-B, BCIPT III and BCIPT III-B, the &quot;Bain Entities&quot;).</footnote>
        <footnote id="F9">Mr. Christopher Gordon is a Managing Director of BCI. By virtue of the relationships described in these footnotes, Mr. Gordon may be deemed to share voting and dispositive power with respect to the shares of Common Stock held by Bain Entities. Mr. Gordon disclaims beneficial ownership of such securities except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F10">On August 10, 2015, the Bain Entities distributed 42,778 shares of Common Stock to one or more members and partners of the Bain Entities in connection with certain charitable gifts made by such members or partners on August 10, 2015.</footnote>
        <footnote id="F11">Mr. Gordon was awarded a grant of 1,611 shares of Common Stock of the Issuer. These shares vest in three equal installments beginning February 26, 2016.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Christopher Gordon</signatureName>
        <signatureDate>2015-08-12</signatureDate>
    </ownerSignature>
</ownershipDocument>
