You should be able to refinance even though your name is not on the mortgage. The lender will ask for a verification of mortgage from your current lender.
First, you name needs to be on the deed. Second, you will need written permission from your husband allowing you to refinance without him signing the loan. (Your lender should be able to provide this form for you.) Third, you will need to qualify for the loan based on your income and credit score.
If you can meet those requirements, then you will be able to refinance to get the lower rate.
In addition to qualifying income and credit wise, you’ll also need sufficient equity. If you’re paying off a second mortgage that was not entirely used to purchase your home, it will be considered a cash out refinance. Conventional loans allow for loan sizes up to 85% of homes' appraised value on cash outs, FHA and VA loans allow up to 90% of the value. Of course, the more equity you utilize, the greater the risk of default. It is harder to obtain underwriting approvals on them compared with “rate/term” loans in which a current mortgage is paid off to obtain a lower rate and payment, or shorter term. More questions? I’d be glad to help, I write loans nationally. Thanks, Ted