Traditionally, the parents names are included on the invite if they were helping to pay for it but it is YOUR day as a couple so don't let old traditions get in your way. I personally like it when the invite says "along with their parents". An example is below.

Anna Lee
and
James Michael
Along with their parents
(can include parents names as optional here)
request the pleasure of your company at their marriage
(details about the ceremony location would be here)

With this, you can also include your favorite poem or saying at the beginning.

Good luck!