You're actually asking a collection of questions, all good ones:
Why doesn't he see your need?
Is his head is completely in the game?
Will he ever voluntarily accept more responsibility?
How can we communicate better?
(And a few others.)
I guess my first question to you is, was the second baby an enthusiastic joint decision? Or did he acquiesce to another child to make you happy? If the latter, then that helps answer the first two questions. Also, I see from your profile that your children are around 2.5 and .5 years. That means you're still tired and probably hormonal, particularly if you are breast-feeding. And I'm guessing that with your husbands history, he was probably fairly "hands-off" with your first child until she was toddling. If that was the case, he's probably also pretty hands-off with the baby.
So, those are tough emotional hurdles for any man (I've known quite a few reluctant dads in my life, one of them being my first husband). Men often talk themselves into a state of self-pity or pure escapism. And they really, really can't imagine how much you've already given, physically and emotionally, to motherhood. Try as they might, they really can't go there, just as most women would never, ever be able to fully imagine being a soldier in battle.
You can't 'make' somebody grow up and be responsible. But you can learn better communication, and you can learn compromise. Or rather, he can learn better compromise – it sounds like you're already doing your share, plus. You are taking his history into consideration, which is good, but is that making you less able to ask for a fair division of duties?
So, let me strongly, STRONGLY, recommend you google Non-Violent Communication and start learning the difference between a true emotion (feeling glad, sad, mad, etc.) and a concept ("feeling" understood, supported, disrespected, taken care of, abandoned, needed, etc.) When we don't understand the difference, we continually throw wrenches into the works of our communications and relationships, because true emotions are spontaneous and completely legitimate, but concepts are always open to interpretation and disagreement.
Non-Violent Communication can be used by only one party to good effect. Learning this very powerful approach is a tremendous help in understanding and respecting the other person's valid needs. By doing that, we reduce their fear, anger and defensiveness, and give them a chance to hear our needs better.
I've used this approach to gently connect with a few difficult people in my life. I've even heard wonderful stories of whole relationships being transformed from enemy to friend. This is good stuff, and worth investigating. You can find descriptions of the basic process, examples, videos, books and classes online.