I have a dilemma!!!!!?

So its my hubby and I 5 yr anniversary this year and I want to go to the beach an all inclusive resort not many in the United States so I want to go to Costa Rica or Jamaica only thing is my husband wasn't born here and he has misplaced his green card so he cant get a passport so where can I start to get this thing in motion so my hubby can get his stuff start and we can get passports to get out of here for a little vaca..