When traveling abroad, the use of credit cards varies by country and region. Taking the United States as an example, usually, credit cards with the Master or Visa logo require a signature (back signature) before they can be used in overseas travel. Used by most businesses, showing proof of identity is a regular requirement. Regular merchants may require ID even if they have a signature. However, in small stores or fast food restaurants, the signature requirements may be looser, and passwords and IDs may not even be checked. I have encountered that even if the Master debit card does not have a signature, you will be asked to provide your ID, and the store clerk may recommend that you sign when purchasing; a credit card may or may not require an ID, depending on the specific merchant, especially It's a small transaction. In some cases, clerks will check notes on the spot to confirm information.
My personal suggestion is that if you use your husband's card, as long as he doesn't check the account and the store clerk doesn't verify it, it won't be a big problem even if the signatures are different. However, for insurance purposes, it is best to have a backup card in case you need to verify your identity, and you can replace it in time if it cannot be used. In general, despite these regulations, as long as you are prepared and communicated, credit cards can generally be used while traveling, but the specific circumstances will need to be operated according to the regulations of the local merchant. Hope this information is helpful to you.