Okay, listen....first, yes, his lying was unacceptable, but you did back him into a corner. Your asking for such a quick turnaround abandonment was also unacceptable. But, you don't have a divorced spouse with a young child, so I don't think you can see things from a different point of view.
You are marrying a man with a child and an ex-wife. He is very recently divorced. Now, there is the smallest of chances he is still intereseted in his ex-wife, but more than likely, he's not interested in her. He just FEELS GUILTY. He doesn't want to see her struggling horrendously and maybe she has medical issues he needs to discuss with you. Maybe he is just waiting until she can get her own to take her off his policy.
My husband and I both have exes with other kids. We BOTH supported small things for our exes in our current marriage, just so our kids wouldn't feel the ramifications of us shutting down small financial support due to stress, loss of home, etc. My husband kept their old house financed in his name, because her income wouldn't qualify for three years until she had an income history. I still, to this day, allow my ex to pay no child support to me, despite the court order, because I know he would have to move to a dingy shack and I don't want my kids to have to do that. We do not ask any child support of my husband's ex despite the fact we have full custody of his kids also. We have given them gas money. We have waived school and medical bills, and many other things. The nice thing is we all have a good relationship with each other and the kids have no fall out. We can afford it right now, so why raise hell about it, just to make a point, or cause jealousy where none should exist?
It's not your responsibility to pay this bill, unless you want to help. If you do choose to help, you need to have clear lines drawn. She does need to get her own insurance very soon, but maybe she is limited by past medical history.
The bottom line is .... him helping support a little bit is not indicative of feelings you should worry about, and should cease and desist if it becomes a relevant, pertinent factor and should have a timetable of expectations.
What is not acceptable is him not telling you. Try not to get angry, just let him know he needs to talk to you and let you be in on the decisions also.
This is his child's mother. He doesn't want his child to suffer because mom can't manage, and, believe me, many people have guilt .... lots of it... after a marriage fails. Don't be jealous...that makes you part of the problem.....be part of the solution, and understanding that his situation is different from yours.
If these are things you don't think you can deal with, you will need to find a man without kids and an ex.