Can I refinance real property where my name appears on the security dead but my now deceased husband is on the mortgage alone?

I am a little confused when you say that you are on the security deed, but then state that your husband is on the mortgage alone. Usually in Nevada, the security deed is a mortgage. There may have been a deed to you followed by a deed of trust in favor of the lender which was signed only by your husband. You could refinance if you can convince the lender that you have the income to make the new payments and qualify for the loan. That is really a question of lender policies, not law. If the current lender won't refinance, then look for new financing. You will need to get the property in your name only by filing a death certificate and affidavit terminating joint tenancy (if you held it in joint tenancy) or by filing a probate proceeding.

This is a complicated issue for you and the Mortgage Company.