It depends. If he lived separately from you for the remaining six months of the year and has a qualifying dependent, for whom he provided at least half of the household support, then, yes, he may claim head of household. (You also would qualify for that same status if you meet those conditions).
If not, then your options are married filing joint or married filing separtate. Here are some FAQ's that cover these topics more in depth:
Can he claim Head of Household:
https://ttlc.intuit.com/replies/4206137
Qualifying Dependent for Head of Household:
https://ttlc.intuit.com/replies/4791157
Married Filing Separate or Joint: https://ttlc.intuit.com/replies/3288477
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