It's not clear exactly what you mean by "separated." If they are "legally separated under a decree of divorce or separate maintenance" then they are treated as unmarried for tax purposes. That means that they cannot file as married filing jointly or as married filing separately. They have to each file as single. Not all states have legal separation. But if they are not "legally separated under a decree of divorce or separate maintenance" then they have to file as either married filing jointly or married filing separately. This is one of the legal issues that you have to resolve.
I am omitting some details about a married couple living apart that involve one or both of them having a child living with them (not an adult child), because that does not appear to be the case here. Simply living apart does not make them legally separated.
