Hospital bill and other bills

So I've been recently getting my bills for my OB visits, ultrasound visits, the few times I had to go to the ER, and finally my hospital bill for labor and delivery. My husband is in the military so we have tricare for insurance. Since he's the sponsor, the bills come in his name. When he gets the bills he hands them over to me. My issue is that I am not working right now and we both agreed that I would stay home with the baby for 3-4 months. We also discussed how any bills I'm unable to pay, he will pay it. With little income coming in from my maternity leave pay, I can barely pay my car note, school tuition, etc, and then make groceries. Am I being selfish for still wanting him to keep his word about helping me with my bills or should I just pay my own bills? Anyone having this issue with their spouse? I feel a husband should never even hand over a bill to his wife without asking if she needs assistance with it.