No, normal case is your or your husband's insurance pays for it
Deductibles can vary wildly depending on someone's insurance plan. However, there are a myriad of financing options, charities, etc if for some reason you can't afford that.
I would estimate the vast majority of people in the US need to budget at least $5k for a baby, if everything goes right. It would be better to have $10k cash though depending on prenatal visits, c section possibility, and multitude of other costs that can arise.