I think most insurance which would cover an OB in a hospital will happily cover a CNM in hospital. Mine covers CNMs out of hospital, too, but not all policies would. Since DEMs are a/illegal in my state, they would not be covered (at least, I think that's true.) But ask your midwife what her experience has been and/or call your insurer directly.
When I first read your post I thought you had a midwife who was a dude named Brad. Oy! Then I had this whole thought stream about how sexist the title Midwife is. Then I thought that maybe it isn't since it reflects a historical role and that women need to reclaim the field of women's health care. Oy the things I think sometimes :LOL