Which tax form do married couples use?

Claiming innocent spouse relief, which applies to all joint filers.

An election to allocate a deficiency, which applies to joint filers who are divorced, widowed, legally separated or have not lived together for the past 12 months.

Equitable relief, which applies to all joint filers and married couples filing separate returns in community property states.

8857 to request any of these kinds of relief. Publication 971 explains these kinds of relief and who may qualify for them.

8332 Release of Claim to Exemption for Child of Divorced or Separated Parents

There are options, depending on specific cirumstances.