I would not send them an invitation since the party is for them and the baby. Invitations should be used just for the guests.
You could send them a "party notice", maybe a nice greeting card to let them know that there will be a party in their honor. I think that would be a nice touch.
You could send them a card that matches the invitaitons, but just change the wording a little. And after the party, you could send them another card, just telling them that you hope they enjoyed the celebration.
Hope this helps, and thanks for submitting your question.