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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2017-07-31</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>200 CLARENDON ST.</rptOwnerStreet1>
            <rptOwnerStreet2></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>2017-07-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>2453764</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>51.65</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>998438</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See footnote</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, par value $0.01</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>8203</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of Common Stock held directly by Bain Capital Fund VIII, LLC, Bain Capital VIII Coinvestment Fund, LLC, Bain Capital (CR), L.P., BCIP Associates III, LLC, BCIP Associates III-B, LLC, BCIP T Associates III, LLC, BCIP T Associates III-B, LLC, and BCIP Associates-G (collectively, the &quot;Bain Capital Entities&quot;).</footnote>
        <footnote id="F2">The governance, investment strategy and decision-making process with respect to investments held by the Bain Capital Entities is directed by the Global Private Equity Board of Bain Capital Investors, LLC (&quot;BCI&quot;). 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 all of the shares of Common Stock held by the Bain Capital Entities. Mr. Gordon disclaims beneficial ownership of such securities except to the extent of his pecuniary interest therein.</footnote>
        <footnote id="F3">Includes 6,182 shares that are subject to three-year vesting conditions.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Christopher Gordon</signatureName>
        <signatureDate>2017-08-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
