Lenders generally will not add someone to a loan after the fact. Mortgages are designed to lock the debtors into the agreement. Also, if the loan has been sold or assigned to another party, the new creditor will be most likely be unwilling to make the change you desire because it bought the loan assuming a certain level of risk for default. Changing that risk changes the calculations behind the purchase price of the loan.
Refinance your home
The only way I am aware of that you can be part of the loan is to refinance. Perhaps you and your husband are in a position to refinance to either a 15-year loan or a 10-year loan. You may be able, given today's rates, to cut your interest rate significantly. Please see the Bills.com refinance savings center to get no-cost quotes from mortgage refinance providers or to find the best home refinance loan available.
Separately, although it still does not show on your report, if you are helping to pay the mortgage, it may help to keep track of any checks you use to make the payments. If you can demonstrate that you have been paying the loan, using canceled checks or bank statements, it may be easier to include you on the refinance, should your income or employment status be a barrier. Often, presenting one year's worth of these records along with a letter of explanation to the lender will demonstrate a level of credit worthiness on your behalf.
Raise your credit score
In your question, you express a desire to improve your credit score. Please read about some steps you can take to raise your credit score, independent of being a party on a refinance loan.
Generally speaking, I dislike the idea of refinancing to add a spouse to a mortgage to increase the spouse's credit score. Please see the Bills.com resource Will Adding My Name To A Mortgage Help My Credit Score? for additional discussion on this issue. The decision to refinance should be based on the financial merits, whether or not refinancing will save you money and improve your position. Weigh the lower interest rate and/or payment of the new loan and the costs of refinancing. These factors are far more important that the potential to raise the spouse's credit score by adding the spouse to the mortgage.
For general information about credit, please review the information you will find at the Bills.com credit resources page.