My great-great-grandmother was a midwife here in the US, as was my wife's
great-grandmother. I don't know if that makes the profession common
amongst Jewish women during the early decades of this century, but I would
guess that it was not unheard of. I know that family lore says that my
wife's great-grandmother was trained in a program at Columbia University,
and I have read of that program in books on the history of midwifery.
(You might want to check "American midwives, 1860 to the present" by Judy
Barrett Litoff, or "The American midwife debate : a sourcebook on its
modern origins" by Judy Barrett Litoff. I don't know if these have the
information on that program or what is in them - just found them listed in
my library's catalog and they look as though they might be useful.)
However, I have never sent a query to Columbia to find out what records
they have on the training program.