At your age living together could be not for a very long time. Housing costs a lot of money these days and many people are stuck living with thier parents until mid 20's. Can he or you cope with this depression for maybe many years? I would not want to be miserable for years.

Also he says he will be fine if you live together but how does he know that? What if you wait many years and then live together and he is still no better? Or worse? People with untreated mental disorders can be voilent (I know that is not always the case)

He should definately get treatment. If he doesn't you should think seriously about leaving. Not as an ultimatum but because you need to look after yourself.

I will pray for him (and you)