Simple answer: When you are married, you always have the option of filing jointly, even when your incomes are very different, or one spouse is out of work or retired. Joint filing almost always results in lower tax because many credits and deductions are reduced or disallowed for married filing separately.
Head of household is never allowed unless you are going through a marital separation. HOH does not mean "head of the family" -- it is a special status for single parents who were never married, or due to separation or divorce.
Your other option is married filing separately. Very rarely, married filing separately is slightly more advantageous because in some states, filing MFS means you pay less state income tax even though you pay more federal income tax. But that is not an issue in Texas, and in other states, the scenarios have to be carefully tested and compared.
