Is it possible for two depressed people to have a healthy relationship?

Depressed: Sure. Both can be supportive of each other, and with proper therapy, they can lead a healthy productive life.

Depression: Each of you need to be addressing your symptoms independently but also I would strongly recommend going to couple's therapy if you need to work on improved communications and expectations. Setting healthy boundaries will help to prevent you from getting drawn into becoming responsible for managing the other person's mood swings and behavior.

Of course: In some ways you both will have an empathy for each others' situation. Some good treatment will help you individually and would likely improve your relationship too. Good luck.

Yes, with support: They can, particularly if they are both in individual treatment, and in couple's therapy, as the need arises. Such a relationship will be challenging, but all relationships are. With appropriate support, this relationship may fare even better, in many ways, than one where one person is depressed and the other is not, given the understanding and experience each party brings to the dyad.