Using The Tax Book Filing Status Chart as a guide.

Was the taxpayer unmarried? - Yes

Did the taxpayer over half the cost of keeping up his or dependent parents home? - since we are not talking about parents here no.

Did taxpayer pay over half the cost of keeping up his or own home in he or she lived? - as I said above I am making the assumption that yes he did.  Continue on.

Did another person live with taxpayer for more than half of the year? - yes child lived with the parent all year.

Was this other person claimed as a dependent by the taxpayer? - No

Was this person an unmarried qualifying child of the taxpayer?  Yes - Taxpayer can file a HOH.

Seems clear to me.  Unmarried parents who lived together all year.  The parent who paid over half of the support can claim the HOH.  The other parent can claim the child and the appropriate credits.  I will attach a copy of the page in another post for you.

@TAXOH @itonewbie