I believe you have to get a visa to travel out of the country to a non-U.S.A region, as a permanent resident of the U.S.A.
You aren't covered as citizens are, in other words.
This means you have to have a passport of your nation of origin and go through the usual process to acquire visa for the nation you wish to visit.
I do not claim absolute knowledge on this matter. I'll advise you to seek further information from appropriate authorities.
Ooops! Sheselectric said it in a little more detail. Indeed, it would depend upon the laws of your nation of origin/citizenship, I believe. You might not need visa if your country of origin/citizenship has an agreement with your country of destination that does not necessitate that you travel with a visa there.