Why not? It's her kid too! :confused:

After my divorce, me and the ex continued to attend the kid's and grandkid's birthday parties and it worked out fine.

Does everybody get along? If they do, I see nothing wrong with it at all. I actually think it's a good idea.

As long as there isn't a bunch of drama between the ex and your husband, then there shouldn't be a problem. I am still invited to different functions from ex sister -in-law for my niece and nephew. I go because those are still my niece and nephew! My ex is getting re-married in a week and I have meet his fiancée and she is nice lady and most important she treats our kids great!
I know you will feel uncomfortable, but remember she is the ex and you are the present. Hold your head high and make your husband proud to have you by his side. Not only will he notice, but your step kids will someday remember the kindess you shown for letting he/her have a great memory of this birthday.

Their kid? Not their child?

I think you are the one with issues, not the child, father or mother.

What is your problem with the "ex" being invited?