I think it depends. As we all know, people shouldn’t converse with the opposite gender, even by writing. If the father is sending out invitations, he should address it to “Rabbi/Mr. Ploni and family”.
However, let’s say there a case where the chosson/kallah has no father involved – either because of a death, divorce, or some other reason. In such a case, all letters should be addressed to “Mrs. Plonis and family”.
The question is what to do if there’s a guest that is single. In such a case, I think a posek needs to be asked as to how to address the invitation. Maybe address it to “Current Resident”?