It depends how formal you are trying to be. Both forms are OK - but putting the Dr. in is a bit unnecesarry?

I think for consistency you either address both formally eg Miss and Dr or neither.
Dr as you know is formal title, so if someone has worked hard for it, why shouldn't everyone know!

I would write,
... invites you to the forthcoming marriage of their daughter Jane to John Smith M.D.

or

... requests your presence at the marriage of their daugther Jane to John Smith M.D.