Take the time to setup your "profile" in Marriott.com and Continental.com Also, here is an excellent "portal" to use @ http://pageonce.com to see all your "award programs" and manage them with one interface. In Marriott.com you would want to have your awards be your airline preference, if I understand your question.
you won't have to show your card, but you can't double dip. So, you can link your rewards card to your continental, but you'll only get points for the continental. Under your reward preferences at the bottom left, click Edit earning preferences. I believe its 2 miles per dollar.