If you a married the ONLY way either of you can file HOH is if you NEVER lived together at anytime the last 6 months of the year ... so if you never spent so much as ONE night in the other's home from July 1 to the end of the year you would both qualify for HOH. Otherwise you should file jointly.
https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately
https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states
https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separ...
