If you are married and live together he can’t file Head of Household. You should be filing a Joint return even if one spouse has no or low income.
Here's a FAQ for Head of Household
https://ttlc.intuit.com/community/family/help/do-i-qualify-for-head-of-household/00/25539
Can a married person file Head of Household?
https://ttlc.intuit.com/community/married/help/can-a-married-person-claim-head-of-household-filing-s...
