Filing Status

Yes, you can both file as Head of Household, if you qualify. (there is no "Single, Head of Household" filing category, just Head of Household).  

(As you complete the Personal Info interview in TurboTax, the program will help determine if you qualify for Head of Household filing status.)

Even if you were legally married as of December 31, you are considered unmarried (and therefore eligible for Head of Household) if all 5 of these conditions apply:

1. You won't be filing jointly with your spouse
2. Your spouse didn't live in your home after June (temporary absences due to illness, school, vacation, business, or military service don't count)
3. Your home was your child's, stepchild's, or foster child's main home for more than half the year (non-child dependents in your home don't qualify)
4. You paid more than half the costs of keeping up your home during the tax year
5. You meet the qualifications to claim the child as your dependent, even if the other (noncustodial) parent is actually claiming the child as a dependent on their return

You can also be considered unmarried for Head of Household if your spouse was a nonresident alien at any time during the tax year and you're not treating them as a resident alien.

There are some exceptions to requirement 3, if a qualifying person lives in your household. See: What is a "qualifying person" for Head of Household?