As far as I know your greencard is only valid together with your passport. My dad always needs to show his German passport together with his greencard when he enters the United States at airports.

Still people, why is it so hard to understand that if you go to a different country that you need a passport. Even in Europe where we have Schengen you still should always carry your national ID (which doesn't exist in the United States and even if US driver licences are used as IDs they are not a national ID) or passport because there can be always random border checks.

OT: I also think it is ridiculous to do ID checks between Canada and the US. The border is several thousand miles long and there are enough places to cross the border without anyone noticing it. Why don't Canada and the US create something similar to the European Schengen-Treaty? It is much easier to control the major ports of entry like airports and sea ports instead of trying to catch people at the Canadian-US border. I don't even want to talk about trying to catch terrorists.