Yes Medicaid will pay CNMs for a homebirth. I have been reimbursed multiple times. CPMs are not currently licensed in Iowa so I would guess it would not reimburse for them but I have no personal experience with that. Hope you find what you are looking for!
My second baby was an in-Iowa, home-born, medicaid-paid baby :) Sadly the birth center with the CNMs we used has since closed, but if you can find a similar set up, it is definitely possible...I don't live in Iowa any more, but I know Kathy Deol in Iowa City is a CNM doing home births; dont' know if she is a medicaid provider though...