One of the lenders we often suggest to client is Pime Lending and Matt Stancato who heads up the Delaware office, had a great piece on the different kinds of mortgage insurance. They offer four kinds.
Single premium MI--a single lump sum paid in advance and partially refundable when the borrower owes less than 80% of the property value.
Single Financed MI--same thing, but financed. Borrower stretches MI over the life of the loan with no monthly payments.
LPMI--for a small rate increase, PrimeLending will pay the MI for the borrower. (This works out best at 85% LTV--otherwise the single financed is the way to go.)
Hybrid--finance part, pay part monthly. Great for borrowers with a set price point in mind. Remember to ask