If you live apart and he has a qualified dependent then he can file as HOH.
He cannot file HOH unless he is claiming a dependent. You say the ex is claiming the child. Without a qualified dependent, your spouse can only file MFS or file jointly with you.
If the two of you file MFS, then you follow the rules which say both of you itemize or both use standard deduction.
Information needed by your spouse:
Am I Head of Household?
https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household
https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household
If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
