I will take a cruise soon, which will leave US to Mexico and then back to US. I am a US permanent resident and a Chinese citizen. Just found that my Chinese passport is expired. Can I still use my expired passport but valid gtreen card for the trip?

In addition, it takes a month or so to get a new Chinese passport from Chinese Consulate in Houston. Do they issue an official travel document such that I could use it for the cruise in case the expired passport is not acceptable? If yes, how long to get the travel document? Many thanks.