If his parents are paying for any part of it they should be included on the invitation. If not, their names don’t appear. The most traditional wording would be:
Col. and Dr. first name middle name last name request the honour of your presence (or “pleasure of your company” if not a religious ceremony) at the marriage of their daughter Capt.first name and middle name (only use last name here if different from yours) M.D. to Capt. first name middle name last name M.D. on full date written out, including year, then at place.
You can include reception invitations in a small card inside the invitation or continue the wording: Reception immediately following the ceremony. If the reception is to be later, then it’s Reception at time at place.
Keep in mind that Brits typically have 2 receptions: one following the ceremony and a fancy dinner later that evening, in which case the earlier reception may be on the main invitation, but the later one will be a separate card.
I understand the man’s name should not be separated from his surname, is that correct?
So: “ Dr. and Colonel Mary and John Smith”
One complication I did not mention is this goes out in English and Hebrew, but that varies by recipient.