What’s the Deal with Refinancing Our Mortgage?

refinancing

I have a mortgage for my home that is 477K and apparently zillow.com says it is worth 447K now….I want to refinance because my husband was working 2 jobs and now he’s working 1 and the bank we have our mortgage with says if we refinance we will have to pay the same amount because we have a 7.125 interest only and we would have a principal and interest if we refinanced….what’s the deal? Is there no way to get our home a better Monthly payment with all the new laws in effect?