Upvote:2
You can enter the US with only your green card; a passport is not required.
As for entering Mexico: Timatic, the database which airlines use to verify passenger travel documents, states that you need both the passport and green card, but the passport only needs to be valid on the day you arrive.
The relevant bits:
Passport required.
- Passports and other documents accepted for entry must be valid on arrival.
- Warning: if departing from the USA (regardless of any destination passport exemptions), a valid passport and/or accepted departure document is required by the US immigration authorities.
Passport Exemptions:
- Nationals of Philippines with an emergency passport.
Admission and Transit Restrictions:
- Passports must be machine readable to enter and transit.
- This does not apply to passengers with an emergency or a temporary passport.
Visa required, except for Passengers with a Permanent Resident or Resident Alien Card (Form I-551) issued by USA for a maximum stay of 180 days.