Since XH and I have joint custody, I am going to suggest we do separate birthdays. While him and I get along okay, my family and friends want nothing to do with him and I really do not want to be around his GF (a former friend of mine whom he had an affair with).
In the future we may try the joint thing, but for his first birthday I think it might be best him and I do separate parties.
Ex and I are on good terms, and we get along with each others' families well. I invited him and his family to our kids' parties until we both came to have significant others in our lives, who also have families that want to celebrate with our kids. So now we do separate smaller parties but our kids are older (4 and 7) and they think it's the best thing ever to have two celebrations.
For a First Birthday, I would definitely include him and his family if things are on good terms because the first cake smash (if you're doing that) is a one-time thing in my opinion.
My XH and I had only been separated for 3 months at DS' first birthday so we had a joint party. Biggest. Mistake. Ever.
That day is what put the nail in the coffin for my decision in filing for divorce.