Please note the following information regarding your proof of legal residence in the USA and re-entry document for the application for a visa to the Schengen States (European Commission Schengen Law):
Original of valid US alien registration card (residence permit aka. Green Card) or valid US residence visa (e.g. type A, E, F plus endorsed I-20 by competent authority, G: H; I; J; plus J1 documents, L, O, R) must be presented. The US residence permit or visa should be valid at least three months beyond the intended departure from the territory of the Schengen Member States.