Head of Household

[Pjacobs]

My boyfriend and I live together. We share one son (H) who was born in 2020. HIS two daughters (Z) and (S) both under 18 moved in with us in March 2020. All 5 of us live in the same house and same address. I claimed (H) on my taxes for 2020 and my boyfriend claimed his two daughters (Z&S) on his 2020 taxes. 
I claimed head of household on my taxes because I paid all the mortgage for the year but my boyfriend paid for the utilities. I filed him as single but is he eligible to be head of household as well? 

[DoninGA]

Since you are both living in the same household only one of you would be able to file as Head of Household.  It would the one who paid over one-half the cost to maintain the household and has a qualifying person as a dependent to claim on their tax return.

See this TurboTax support FAQ for HOH - https://ttlc.intuit.com/community/family/help/do-i-qualify-for-head-of-household/01/25539

[Opus 17]

You have one combined household, so only one person can be the "head" of household for tax purposes.  That is the person who pays more than half the total household expenses.  Total household expenses includes rent or mortgage, utilities, insurance, repairs and maintenance, property taxes, and shared food, but does not include personal expenses like clothing and medical care.  

It sounds like you did everything correctly, and there is nothing you can modify to improve your position.  Your only other option would be for the BF to claim all three children, which would force you to file as single, and the BF probably must still file as single as well if he does not pay more than half the household expenses.  In rare cases, he might get a tax benefit (like EIC) that is more than the tax benefits that you would lose, so the only way to know for sure is to test the possible combinations. You can't ever claim your BF's two children unless you either get married, or he is not a "taxpayer" (meaning his income is enough that he does not file, or he owes no tax and only files to claim a refund of withholding and claims no other dependents, deductions or credits.)

[Mike9241]

it may not be possible for the boyfriend to claim H.  since both are his parents the tiebreaking rules are:

the parent with whom the child lived the greater portion of the year. this seems to be a tie.

the next rule is the parent with the highest Adjusted Gross Income

[Opus 17]

@Mike9241 

Those rules only apply to “children of divorced or separated parents”, where the parents live apart. When the parents live together, they can simply agree on which parent will claim the child.