Hmm. Actually I think a major part of you being attached is the fact that you've made your depression into a person. A constant companion of sorts. Maybe... think of it in this way?

There are two of you right? Yourself and your depressed self. Let's call them Positive and Negative for now. Both of them can affect each other though so lets say that Neg keeps Pos feeling bad enough that instead of being positive she turns Neutral. Or even in worse cases she starts to become Negative too. But you know, the same can apply the other way. You can make that poor girl happy You can make them Pos and Pos.

To be honest though your double will always be there inside your mind but I guess that this time, you get to take care of her and really teach her how to be happy and then you can both be happy. Instead of her thwarting you and you becoming unhappy. Does that make sense?