Personally, that's a no-no. If someone my family continued to socialize with my ex-husband, I would probably back away from that family member and minimize my own contact with that person. I would not attend events like Christmas or Easter if chose to invite him. I don't need my post-divorce life intermixing with the ex. I just don't know how he would interpret anything I do you what he hears from family. He has come up with tall tales in the past. He doesn't need to know my personal life. I expect family to treat him nicely and I don't care if they talk occasionally, but full friendship is no longer.
There are occasions where we have to share airspace, and I realize when the kids are older, graduations, weddings, baby's first birthday, there will be more family mixing, but that's the only time I see this as acceptable. I don't socialize with his family but for the rare occasion. I lost them in the divorce and that's okay.
If there's any event around the kids where the families blend, that's fine and that's where my comfort zone ends.
Now because they are still living under the same roof, this brings up another issue of still attending events as a family. I just don't know if it would be wrong to not invite the ex-husband since they are still living together. I would prefer not to, but etiquette-wise, just not sure about that one.