In almost all cases, joint filing will result in the lowest taxes. Married couples are always allowed to file jointly even if they live apart or their incomes are very different. You are not allowed to file as "head of household" because, even though you lived apart, this is considered a "temporary absence due to special circumstances."
The IRS says,
Temporary absences. You and your qualifying person are considered to live together even if one or both of you are temporarily absent from your home due to special circumstances such as illness, education, business, vacation, military service, or detention in a juvenile facility. It must be reasonable to assume the absent person will return to the home after the temporary absence. You must continue to keep up the home during the absence.
Married filing separately is almost always the worst filing status because many deductions and credits are reduced or disallowed.
