Some questions to consider, even if you don't feel comfortable answering them here:
What form of mental illness is he suffering from? What are the symptoms? How do they impact on him and on you at the moment? What treatment has he received in the post and what is he receiving now? How well is it working?
Has he ever harmed himself or anyone else? Had he any plans to do so? Does he smoke, drink to excess or use drugs?
Is he in work? Are you in work? What support networks do you and he have?
There are a huge number of complexities to consider. Situations can be very, very different. Someone who has suffered badly in the past but who has engaged fully with treatment, made good progress, is in a steady job and has solid friends and family connections to back them up is a very different prospect to someone who is poorly but doesn't want to seek help, can't work, is isolated from friends and family and has a recent history of self harm and assault on others.
1 in 4 of us experience mental health problems in our lives. The vast majority manage to be good parents, despite the stresses and changes that a child brings. Whether now is the right time is a judgement call, however.
I would be concerned that if he can't be present as much as you would like now, then it's very unlikely he's in a position to be a supportive partner/father. I think I would advise waiting until he's fully present and enthusiastic, then giving it another 6 months to make sure he's really in a stable place.
How would he cope on 3 hours sleep a night? How would he manage if traumatised by seeing you give birth, and then he had to be main carer for the baby if you weren't able to? How would you manage with the baby if he were to have another bad episode? Do either of you have difficult parent to add to the mix? I'm not saying these things to say that you shouldn't do it, but you should be aware of and try to plan for such eventualities.