Our son was delivered at a hospital by a midwife that was part of a team of 2 midwives (CPNP/CNM) and 2 doctors (OB/GYN). If things got beyond her capability she could call in the doctors for backup. Our daughter was delivered by one of the doctors due to him being on call.

So, nurse midwifes do deliver in hospitals. I actually think they are not allowed to do home births or they can lose their license.

(In the US)