It's different in different areas, and it's different amongst midwives and their particular practices.
Mostly, around here, midwives are hired by physicians to work in their practices. They are not hospital employees (unless the entire practice is a hospital operated charity type clinic). They admit to the hospital.
In Georgia, they still do not write prescriptions (although we're the last state, and they can call in stuff to the pharmacy
: ). As far as how often they consult, and what they consult for, that's up to the individual midwife/physician agreement. There are some obvious things....if a patient needs a c-section, obviously, there's a consult. But, even then, things vary. In some practices, the midwife leaves when the c-section begins, and she is the patient's care-provider after the 6 week check. In other practices, the midwife assists in surgery, sees the patient postpartum in the hospital, and then sees them in the office for the post-surgical check. It just depends on the practice.
Edited to add:: This is solely my experience with CNMs in Georgia. State by state varies, CNM vs CPM vs direct entry all vary. There are very few CNMs in Georgia that do homebirths (cause there are very few physicians that will back them, and it's written into the CNM standards of practice that you have to have a backing physician), so I don't have experience with that.