(This is addressing Mortgage Insurance that is offered by the lender at the time of purchase).
Mortgage Insurance is meant to cover the lender and will decrease over time and your monthly premiums will remain the same. If you pass away, the money goes to pay off your mortgage and eliminate the risk to the bank. Term Life Insurance is meant to protect the homeowner and is usually much cheaper than Mortgage Insurance. If you pass away, the money goes to your family (not the bank) and they get to decide what to do with the death benefit.