My good friend is having a birthday party this weekend and he asked me for advice on the protocol for inviting guests. He wasn't sure what to do in terms of inviting his two best friend's who are in the midst of a nasty divorce. He asked if it would be appropriate to invite them both because they're equally important to him.
I told him it absolutely was appropriate to invite each of them and that it was personally up to them to determine how to handle social events going forward. After all, my feeling is, if you were going to invite them as individuals had they not ever been together, you can invite them now as such. Extending an invitation is a gesture not a demand and it isn't worth the risk of potentially hurting someone's feelings by excluding them on the guest list.
Now, as the couple, if they are in a situation where they can't stand being in the same room with one another without verbally assaulting one another, then they clearly need to steer clear of social situations. In this case, they need to agree upon who would go and who would graciously bow out. And if they can't agree, then they both don't go. Period. It's up to them to be mature enough to put their differences aside in an effort to support their mutual friend or relative.