The mortgage insurance the questioner mentions shouldn't be confused with home owner's insurance, also known as hazard insurance.
When purchasing a residential home that is going to be owner-occupied, mortgage insurance is usually required on first mortgage loans for borrowers who have made a down payment that is less than 20% of the home purchase price. This mortgage insurance, unlike the hazard insurance that protects home owners against property damage, protects the mortgage lender against payment default for the coverage period.
There are five different types of mortgage insurance based on the funding source (FHA, VA, non-government) and payment type (Upfront, Monthly, Tax-beneficial). They are:
PMI: Private Mortgage Insurance
PMI is required by conventional mortgage lenders who make non-government insured loans. PMI can be paid in one upfront lump sum (one-time PMI) or in monthly installment payments. Monthly PMI premiums can be done away once the owner's equity in the house reaches 22% or above.
MIP: Mortgage Insurance Premium
For government insured FHA (Federal Housing Association) loans, the mortgage insurance premium (MIP) is required
For Veterans Administration (VA) loans, a funding fee is collected in lieu of mortgage insurance.
TAMI: Tax Advantage Mortgage Insurance
Instead of making either an upfront lump sum PMI payment or regular monthly payments which are both tax-unfriendly, borrowers can choose to opt for TAMI. Under TAMI, the PMI is factored into the interest rate offered to the borrower. This option will definitely increase your monthly payment, but offerers tax advantages as mortgage interest payments on a primary residence are deductable from income.