Maybe I can offer some insight - I have been badly depressed like your fiancee and one of the things it caused me to feel was unworthy of my relationship with my wife. I was very down on myself and felt like my troubles would be a burden to her and i didn't want to drag her into my problems. But more than that, in my depressed state, I couldn't understand why she ever wanted anything to do with me. I could not see any joy I might have brought her, I could only recall things I'd done wrong, and times that I'd failed her, or been unkind to her in some way.
I know she struggled with the situation much like you are, and I think the way she handled it was ideal - in a very subtle way, she just made sure I somehow knew she was there. Her presence meant a lot even though it probably didn't seem like it to her. She didn't try to get me to open up to her or make a lot of suggestions. Eventually I got to a point where I wanted to talk to her about everything and it was a very powerful, emotional and memorable time for both of us.
I believe you can get through this, keep the faith!