People with a green card need a passport ???

If a traveler has the "Permanent Resident Card" and the person is originally from Mexico, he / she can use their "Permanent Resident Card" to cross the CBX bridge. But if he / she is of another nationality, not Mexican, he / she must also provide a valid passport to cross when entering Mexico.

To go out to Mexico yes

To enter the United States, you only need to show the plane ticket and the Green Card and pay 15 dlls