All of the prenatal care is considered your medical expense, not the baby's. And, of course, your own insurance policy is going to cover your own medical expenses. (As long as maternity is covered on your policy, of course.)

The delivery and hospital charges should be considered under your policy too. Presuming that you plan to add the baby to your medical coverage at work, you'll want to complete the necessary paperwork with your employer within 31 days of the baby's birth.