I'm totally unhappy in a not healthy relationship with someone that is depressed
Why do you think your partner is depressed?
They show all the symptoms
If the person you are with is always in a down mood, it is understandable that you would not be happy in the relationship. You should talk to  your partner about how the relationship is affecting you, this will allow your partner to know how the relationship is being affected by his/her mood.
I'm not going to tell him/her that. I have been through it before and it made them feel bad... They get insecure.
I think you both need to communicate your feelings to each other. And if you can try to help them find some professional therapy, they sound like they are really suffering.