There are 2 typical forms of mortgage insurance (which protects the lender from non-payment by the borrower). MIP is collected on FHA-guaranteed loans and PMI is collected on conventional loans, in either case when the amount borrowed exceeds 80% of the value of the property.
MI payments can be deductible for Federal tax purposes, so in a small way they're similar to interest, which can also be deductible.
Avoiding MI often turns out to be an exercise in futility. Years ago it was actually advantageous to avoid the MI, first because MI was not deductible and second because it was a whole lot easier to get a second lien mortgage loan.
When you get your GFEs for both scenarios, compare them carefully. You will probably find that the bottom line monthly payment is practically the same, but it could be substantially worse with PMI if your credit scores fall between 620 and 630. The cash to close can be smaller with 2 mortgage package, but often borrowers elect to roll the upfront MIP into their loan balance and pay a little bit more to reduce their cash requirements at closing.
So, if it costs more per month to have MI, why do that?
Because the interest rate on the second lien will never change. The total payments for both scenarios with and without MI are practically the same monthly because the interest rate on the second mortgage is often very much higher than the first. The reason is simple: the insurance you're avoiding is effectively built into the second mortgage interest rate. They're at risk and they demand additional interest to cover that risk.
After you pay down the loan balance on the loan with MI to 78% of the property value, the MI premium can be discontinued. This can take several years to get to that point, but the higher interest rate on the second will not change at all, ever. So, if the bottom lines of the GFEs look similar, remember that the MI will eventually go away, but the second lien payment will never go down.
In name you can avoid paying the MI, but is that really in your interest? Study the GFEs and ask your loan officer.