Is it possible to consolidate two mortgages into a single payment with a lower interest rate?

It is something you can do; the question is whether you will meet lenders’ guidelines for refinancing. Since that is very fact-specific—it depends on your home’s current market value, your equity in it, your income, etc.—there’s no way to answer in the abstract. You won’t know whether you can refinance until you apply.

Here’s some general information that may be helpful.

First, what you want to do is not just refinance. What you’re looking to do is to consolidate the two house mortgages so you have a single, consolidated payment—preferably at a lower interest rate. Since generally speaking, mortgage rates right now are lower than you describe—in particular, they’re lower than your second mortgage, if you qualify, you probably can lower your rate.

When you refinance a mortgage, what you’re doing is taking out a new loan or mortgage with which to pay off the existing one; you then owe only on the new loan. It’s the same principal with consolidation, except you’re taking out one loan to pay off and replace two.  

In addition to very likely getting a lower interest rate, you might can adjust the length of the loan—make it shorter, to pay it off more quickly and at less total interest, though higher monthly payments; or make it longer, to pay less per month but more in total.

Depending on your situation, you may even be eligible for some federal assistance, such as under the Home Affordable Refinance Program (HARP), which is administered by the Department of Housing and Urban Development (HUD) under the Making Home Affordable Program. It’s worth looking into.