Use your name and your fiance's name.
You are invited to celebrate in the marriage of Betty Smith and Brian Thompson on such and such a day, place, etc.
Leave off parents names, etc. Its not about who is helping or who isn't helping, its about making it easy while not stepping on anyone's toes. parents who insist on being on the invitation should understand that this is the best way
to avoid hurt feelings......
Just use the name of the bride and groom.....now you could add on the RSVP card,
Mr. and Mrs. Bob Smith, Mr. and Mrs. Ken Thompson are looking forward to seeing you on our special day. That let's their friends know who they are...sometimes people don't recognize the bride or groom's name, so this is a nice way around
listing a dozen people who might help or might not help.