It seems to me that we need to file jointly. My state return only offers me two choices: single or married/filing jointly (even if only one spouse had income).
1040 wants me to enter an occupation for my wife. Suggestions offered by 1040 are student or homemaker. She is a student AND a homemaker. I am not claiming her as a dependent.

She is NOT your dependent; she is your co-filer.

You can put EITHER homemaker, housewife or student. All are equally valid.