Usually when green card application gets approved, INS stamps one's passport and that stamp is sufficient for travel.

The stamp says "processed for I-551 temporary evidence of lawful admission for permanent residence. valid until ..." and also has date, location and INS officer #.

If your dad has that stamp he is good to go, if not perhaps he can try to visit his local INS branch and request it.

Perhaps his "resident alien" visa works in the same fashion, if it states clearly that he is a permanent resident there should not be a problem.