@michelejosephine: First and foremost, the absolute rule of addressing people, is that you use the names by which THEY wish to be known. All other rules and guidelines are for situations where you do not know their preference. Their preference trumps all the other rules.
Second, the outside envelope is a business document between you and the postal service; serving the purpose of a contract whereby, for the price of a stamp, the postal service agrees to deliver the envelope to the person and place you specify. The envelope addressing should conform to the post office specifications, and the addressee’s business name (not their social name) should be used. Do not omit the title unless you know that the addressee is on a first-name basis with their letter-carrier and mail-sorters. In Canada, Australia, England, and the rest of the English-speaking world outside the U.S.A., address the outer envelope to the ONE person in the household responsible for maintaining the household’s social calendar, typically the lady of the house. In the U.S.A. address it to both parties of a married couple. When using a lady’s given name as part of her address, the title “Mrs” should be replaced by the title “Ms”.
Third, when using “Sr”, “Jr”, “III”, “II” and so on, the eldest male does NOT take a title. “Mr John Smith” is automatically the most senior one (subject to rule one, above). The Title “Sr” is used only for a widow who goes by her husband’s name. For example:
Mr and Mrs John Smith, a very-old-fashioned couple, have a son, John Smith Jr; and a grandson John Smith III. When John Smith Jr marries, his wife is Mrs John Smith Jr, at least in the minds of all his mother’s friends who are as old-fashioned as she is. When Mr John Smith the grandfather dies, his widow becomes “Mrs John Smith Sr”; the son becomes “Mr John Smith (dropping the “Jr” because he is now the eldest of that name) and the grandson becomes John Smith Jr, being promoted from “III” to “Jr”. (Mrs John Smith Jr would also have dropped the “Jr”, but she finally grew a backbone and started telling her inlaws and their friends to address her as Ms Jane Smith, thank you very much.)
Fourth, the old rule of “ladies first” turns out not to be universally proper. Surely no gentleman, approaching a mine-field to be crossed, would gesture to his wife to precede him saying “my dear, ladies first!” Similarly, a man goes first when crossing a crowded dance floor or restaurant, in order to make way for his lady; and a man goes first when dangerously crossing the continent exposed together on the back of an envelope. (No, I am not making this up. In formal public address it is man first then lady; in intimate informal address it is lady then man.)
So, assuming that your fiance’s mother does not prefer to be called “Mrs John Smith” and assuming your fiance’s father does prefer to be called “Sr” even though he is still alive, the correct address on the outside envelope would be:
Mr John Smith Sr and Ms Theresa Smith
The correct address on the inside envelope would, assuming a formal invitation, drop the first names: Mr and Mrs Smith Sr
The correct address on an informal note of invitation would drop the surnames and reverse the order: Theresa and John Sr