if you could claim the child as a dependent but allow the other parent to claim them you can still file as head of household. here are the rules from IRS PUB 17
Head of Household
1. You are unmarried or considered unmarried on the last day of the year. See Marital Status, earlier, and Considered Unmarried, later.
2. You paid more than half of the cost of keeping up a home for the year.
3. A qualifying person lived with you in the home for more than half the year (except for temporary absences, such as school). .....
How to file. Indicate your choice of this filing status by checking the “Head of household” box
on the Filing Status line at the top of Form 1040 or 1040-SR. If the child who qualifies you for this filing status isn't claimed as your dependent in the Dependents section of Form 1040 or 1040-SR, enter the child's name in the entry space at the bottom of the Filing Status section. Use the Head of a household column of the Tax
Table, or Section D of the Tax Computation Worksheet, to figure your tax
