married filing single if claiming foreign income, spouse filing head of household, can i file single

I am a US citizen who works and lives in another country (bonafide resident ) and i claim foreign income exemption (2555). i am away from my spouse (US resident) and kids for most of the time, between July and December, we lived apart but i visited twice for 15 day each. (30 Days)...

 

QUESTIONS

1)can my spouse file as Married in marital status and Head of Household (HOH) in filing status ( claiming the kids  and provided more than half their care and they reside with my spouse).

 

2) while i file as Married filing Single (since my spouse is filling HOH)