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
