A green card is the term for a Permanent Resident Cardgranted to a foreigner by the U.S. Citizenship and Immigration Services. The card gives the holder the right to live and work in the United States permanently without restriction. With this card and your foreign passport, you are allowed to travel outside the U.S. and return with no additional paperwork.
According to the U.S. Embassy of Mexico, all legal residents of the United States, regardless of their nationality, can travel to Mexico if they are in possession of a green card (now they are pink.) One does not need to go through the process of applying to Mexico City for an entry permit nor do they need to have their passport stamped. A tourist card can be issued on board an aircraft or the port of entry to be able to travel to Mexico as tourists, in transit or for short business trips. You must carry a valid passport and your U.S. Permanent Resident Card (green or pink card) issued by the United States government at all times.