I am sorry to hear about the passing of your husband. Since there is a mortgage on the property they will require monthly payments to avoid the possibility of Foreclosure. Even though you are not on title the property will go into your husbands estate, so if you are his beneficiary everything (debts included) become your responsibility.

is a traditional mortgage or a reverse mortgage?

You are not responsible for the mortgage, meaning that any late payments or even a foreclosure will not show up on your credit report. If you want to stay in the house though, you will need to keep the payment up to date, or the bank will foreclose.