Hello William, and thank you for your question. FHA does allow you to refinance to 96.5 percent,but I would not recommend that because of its high mortgage insurance costs. VA loans, if you're eligible, allow 100 percent. And while you might be able to wrap your first and second mortgage together with a cash-out home loan, mortgage insurance and the fees associated with this kind of refinance could easily wipe out any benefit that you get by reducing your interest rate. I assume that your first mortgage does not have mortgage insurance, and that your second mortgage is about 13 percent of your current me value, for a total of 93 percent. Feel free to write back if this assumption is incorrect.
Now, I don't know what the "high" interest rate of your second mortgage is, so that makes it a little harder to advise you. I do know that it's a lot easier to get a second mortgage to a 90 percent loan-to-value than a 93 percent loan to value. Would it be possible for you to do a "cash-in" refinance, bringing cash to the table and lowering combined the mortgage balance to 90 percent? Other options depending on your credit rating and how bad your mortgage rate is include personal loans, or a zero-interest credit card (you have to pay it off in 12 to 18 months to get zero interest) to bring you mortgage balance down to a level at which you can refinance.
There are many factors involved in this decision -- your blended rate (the combined rate of your current first and second mortgage), the presence or absence of mortgage insurance, your credit rating, and the costs of refinancing all play a part. If you'd like to provide more information, I can give you a more detailed answer. Thank you for writing.