How do we word the announcement with divorced parents, one of whom is remarried and one of whom has a long term significant other?

Your PARENTS are announcing your graduation from college? You are not?

Anyway, it's "Mr and Mrs X" (father and step parent) and Mr OR Mrs. X are pleased to announce -

The long term relationship has no standing here.

I think it would depend on the relationship of the graduate and the step parent. If there is a parental relationship between them, then:

Mr. and Mrs. John Smith and Mr. and Mrs. Mike Jones ... or Mr. and Mrs. John Smith and Mrs. Nancy Smith...

If there is not a real parental relationship then:

Mr. John Smith and Mrs. Mike Jones....

OR if you want to simplify it, you can say:

The parents of Mary Smith... or The family of Mary Smith