Typically debit cards are run as credit when used online, so it's effectively a Mastercard or Visa with different payment terms on the back end. You should have all the same rights and features as any other Mastercard or Visa for those purchases.

I agree with the other fellow that you should avoid using them, though. You may have the same rights, but the potential consequences are different. A credit card which you pay off each month provides the same basic functionality but with more safety. Plus you get to make 0.01% of interest off the float.