Hi Confused Refi Shopper:
Both mortgage companies are “sort of right,” but this deserves elaboration.
To begin, there are generally two types of refinances for conventional financing, which is what you seek. The conventional route does not require the upfront loan insurance payment as you mentioned.
This synopsis is going purely with conventional guidelines in mind. Lenders have the ability to overlay additional guidelines on top of the already-existing guides.
Conventional loans fall into either a Limited Cash-Out refinance or Cash-Out refinance.
Limited Cash-Out (a.k.a. Rate/Term) refinances are eligible for conventional financing with mortgage insurance. Cash-Out transactions do not allow for conventional financing with mortgage insurance and require the use of the FHA program.
The transaction of combining the two mortgages, for your scenario, is eligible for the Limited Cash-Out classification as the second mortgage (HEL) was used to purchase the property. Looking ahead, the second mortgage will be verified as purchase money by providing the settlement statement (HUD-1) obtained at the purchase’s closing.
The HEL acronym is indicating that it is a Home Equity Loan, instead of Home Equity Line of Credit (HELOC). This just means that your second mortgage is not eligible for draws. Instead of revolving, it is closed-ended.
Past conventional guidelines allowed the second mortgage to be combined under a Limited Cash-Out heading if the HEL/HELOC was “seasoned,” which means it went without draws for at least 12 months. That guideline has since been updated to allow only purchase money second mortgages to be combined under Limited Cash-Out.
For the specific guideline regarding your scenario, feel free to direct the loan originator to B2-1.2-02 of the Fannie Mae Selling Guide.
Full disclosure: the conventional mortgage insurance is only removed with a request to the lender at 80% LTV. At 78% the mortgage insurance is automatically cancelled. This falls under the PMI Cancellation Act.