Z - I don't know how it works in the U.S, but I'll tell you how it works in Canada. We can chose to use doctor or a midwife - I think maybe all or at least most provinces now have midwives covered by medicare, so it's just a personal choice based on what sort of birth you want. If you have a high risk pregnancy, most midwives will transfer care to a doctor or at least share the care with one. I started off my twin pregnancy with a midwife but ended up with a twin specialist OB.
You see you OB or midwife throughout the pregnancy, and obviously at the birth, but if you have a doctor, once the baby is born and you are deemed healthy enough to leave the hospital, their care is done other than a 6 week post partum check-up. You bring your baby to a family doctor or pediatrician for regular visits. I think the home visits are one of the best perks of having a midwife. Who wants to pack up a newborn baby, especially in the winter, and go to a doctor for check-ups?
With a midwife, however, she will come to your house to visit for the first week or so after the birth, then you go for regular visits to her office until the baby is 6 weeks old, after which time care is transfered to your family doctor or pediatrician.