Billing with your clinic?

Does anyone have global billing with their clinic? I was bombarded at my first appointment with my first pregnancy with a contract to sign saying I would pay 1/10 of my deductible every month until delivery so my bills would be paid when I delivered. I was sort of caught off guard and had no chance to even think about it or anything. After signing I was told that when I get to the hospital to deliver, the hospital would also ask for my deductible since these payments I’m paying now will not have been applied to my deductible until after delivery. I am not ok with paying $6000 out of pocket when my deductible is $3000 and having to deal with being reimbursed while caring for a newborn. Is this the new thing?