I have a son and my roommate has a son, we are not related. We share all expenses equally. Can we both claim head of household

[LeticiaF1]

Only one person per household can claim the status of Head of Household. 

To qualify for Head of Household you must meet the following qualifications:

1. Were unmarried as of December 31, 2023 and
2. Paid more than half the cost to run your (or a qualifying parent's) home this year (rent, mortgage, utilities, etc.) and
3. Supported a qualifying person.

Since neither one of you paid more than half, you won't qualify for Head of Household.