I think I would go ahead and invite them and not worry about it. It will be awkward for a time but it might also be good for the three of you. Inviting them will show them that you have no hard feelings and you've moved on. I think that's the right thing to do to keep the peace. They might not show up but but it won't hurt to invite them. Just shows that you're the better person. Just smile and have a good time.
