Hi there,
I'm so sorry this has happened to you, it must be such a shock 
I'm actually in somewhat of a similar situation myself at the moment; my ex partner has behaved with absolute cruelty since he decided to leave me when I was ten weeks pregnant with a planned baby. I haven't spoken to him in three months and he's in a relationship with someone else now who may or may not, the former being more likely, have been in the pipeline when he chose to leave, so I really mean it when I say I know how you feel and I can only hope that your situation works out differently to my own, though I would advise you to tread carefully with how much trust you put in him, as harsh as that may sound.
It's a difficult thing because you have to be careful when choosing to believe what he says; I've found that actions are much more of an indication of what someone intends or wants to do. I would say that if he's genuinely serious about having couples counselling and that if his depression is something that is playing an active part in his behaviour at the moment, then he should be the one to arrange appointments etc in order to demonstrate that he means what he says. If he does, then it could definitely be worth a go.
Have you had any contact with his family at all? Do you know where he's staying at the moment? Has he said anything about financial support, or the baby for that matter?
Take the support you're given with both hands and hold on tight. I can't tell you how much I've needed it and how much it really does help to have someone just sit with you and let you cry, among all the other things that people will want to do to help you.
Unfortunately, it really is a day by day process. I won't lie to you and say it gets easier, as some days I still want to curl into a ball and cry, but you'll be surprised as just how strong you can really be. 