When you get married, your finances tend to intertwine. Separate credit cards, and their effect on your respective credit scores, are one exception to this rule. Only joint cards affect both of you. A card solely in your husband's name has no effect on your score at all, but this doesn't mean it can't affect your ability to borrow.
Social Security Numbers
Your credit is tied to your Social Security number. When you apply for a credit card, the creditor uses your Social Security number to access your credit report. Only transactions made under your Social Security number appear there. If your husband takes out a credit card in his name alone, it won't appear on your credit report because you don't share the same Social Security number.
A credit card in your husband's sole name is entirely his contractual obligation, as well. If you use the card to run up a high balance, the fact that you're married does not usually allow the creditor to look to you for payment. If the card is in your husband's name, he's the only one responsible for the balance, at least as far as the creditor is concerned. Some exceptions may exist in the nine community property states.
Applying for Joint Loans
Although your husband's credit card can't have any effect on your credit score, it can affect you if the two of you apply for a joint loan. In this case, the lender would pull both your credit reports. If your husband's credit card has a history of delinquent payments, this would appear on his report. Different lenders have different procedures for qualifying joint loans, but some look only at the credit report of the borrower who earns more. If this is your husband, and if his payment history with the card is poor, it could affect the interest rate of your new loan, or even prevent you from qualifying. Some lenders will look at the lowest of your respective credit scores. If your husband's credit card history gives him the lower score, this could also affect your ability to qualify.
Benefits of Jointly Held Cards
Taking out a joint credit card can improve your husband's score if his existing credit card has a negative payment history. Likewise, if he has always made his payments promptly, but your own credit is a little iffy, taking out a joint card can improve your score. However, this depends on paying the joint card promptly each month.