Soso,
I suffered from depression for a long time. It is a terrible illness, but for most people, it is manageable if you work at it and get good treatment and support. Is your DP working at it? Is he accessing support and treatment (other than you)? Has he tried or will he try therapy? I do think you are entitled to expect-demand-this much from him. Has he even had a proper diagnosis of depression?
It sounds from your post as though he is putting the onus on you to keep things going and blaming you for how he acts and feels. If he is that is cruelly unfair. It is also guaranteed not to help him recover from his illness. You generally get better by taking responsibility and opening up, not by oppressing other people.
You can't save him and you can't be responsible for managing his illness-that's very much his job, especially now you both have a child.
Actually it sounds as though he is being very unkind and even a bit weird about the cleaning. If he wants the house to be cleaner, is there any reason why he can't do it himself?.
Please look after yourself and your child first, and don't accept 'depression' as a reason to treat you or your child this badly, because it just isn't. It may not even be the cause.
Don't let him just forbid you to see friends during the day: you know this isn't acceptable in any marriage or any circumstances.
Hard though it will be, in your shoes I would have to tell him that you can't just keep pandering to him and until he tackles the depression properly, he's on his own with it, and I say that as a sufferer.
Most of all, don't feel guilty and don't accept the blame whenever he's not feeling happy. It doesn't work like that.