married filing separately can claim head of household

i am married but living apart for spouse. can both of us claim HOH filing married filing separate returns. I have a 28yr old that is my dependent that meet all the qualifying requirements except being under age 19 or 24 not a full time student . Turbo tax is changing status to HOH from married filing separate. Is that correct. My spouse has a 23 yr old son. not a student but meet all but age. and turbo tax is recommending hoh. The numbers are much better. not sure on witch filing status