I am a Mexican Citizen and a US Permanent Resident. I bought a round trip ticket because of a family member's death I only had to show Mexican ID and birth certificate to go there.
What will be sufficient ID for me to come back?
The USCIS or whatever they are called now say that a "foreign national or alien entering the U.S. is generally required to present a passport and valid visa ..., unless they are ... a lawful permanent resident of the U.S. or a citizen of Canada."
That's the theory. The more difficult part will be to convince the airline representative to let you check in. In my experience they are very strict about proper documents, because the airline will be fined and has to find a seat for anyone who gets refused at the border. But maybe in Mexico they are used to people travelling on Green Cards.