My fiance and I are not sure how to address ourselves in our wedding invitations.

The invitation response cards are being mailed to her apartment.

Should we include both of our names on the envelopes?

Like this?

John Doe
Suzy Sue
1234 Easy Street
Ann Arbor, MI 48103

Yes that would work, or just have it addressed to her if you don't live together, I don't think it really matters, no one will even notice how the RSVP's are addressed.

I agree, have her name only on the address.

Tradition states that the invitations are sent by the brides parents (they used to pay for the wedding) and replies are sent to them. Therefore, I would just put her details on it.

Most people are happy to over look wedding traditions as long as you don't act like an idiot, so don't worry.

Miss. or Ms. Suzy Sue. You don't need both names. Both names gives the impression that you are already living together, which will not sit well with some guests.