If your mom is on the mortgage, it means (probably) that she co-signed when you bought your house. The lender may have required her to be on the mortgage because you (and perhaps your husband) didn't have sufficient income or credit to purchase the house alone. Lenders are very reluctant to remove someone from a mortgage. As the previous answer suggests, refinancing into your own name(s) would do the job. But...why do that? Being on the mortgage doesn't entitle anyone to ownership; the deed does that. If the loan is OK as is, just leave it alone.
As for putting your husband's name on the need--making him an owner of the house (along with you), that's very easy to do. See a lawyer. But also check with the lawyer regarding whatever your underlying concerns are--whether it's estate planning (making sure the house goes to the surviving spouse upon the death of one) or asset protection, or whatever. Address whatever your underlying concern is before taking that step. There might, in some cases, also be tax implications.
Again, see a lawyer.