Your hormones are probably all over the show so this is the last thing you need right now. If he really wanted to though he would want you to be involved and he would be telling you in detail what he is doing to get help. He needs to go to the doctors himself and get counselling and help to try and recover.
In regards to what you say about yourself to the doctors I am not sure how they deal with this – I guess they get it all the time new mums getting PND etc so dont be worried about telling them how youre feeling, they may get you help.
Might be worth going to see what they can do for you, i wouldnt tell them about your partners issues, as its for him to sort not you.
Just remember you arent to blame here and nothing you say will make him get help he needs to want it.
Good luck, be strong. xxxxx