My husband is a perm. resident and does not have a cuban passport, 2 months ago we traveled all of Spain, Italy, England and Croatia, He went using a re-entry permit that you can get on USCIS website I believe it is form I-131, re-entry permit. This works to allow him to re-enter the US legally. We had no problems AT ALL! He only had a problem in Croatia where they sent him seperate from me and gave him a 2 day visa at the airport. Also, before we left about 1 month before to be exact he went to the Italian embassy (Since we were going to spend the most time in Italy) he had to leave his re-entry permit along with some photos and show proof of travel along with proof that you have enough money in the bank, in about 2 weeks he went to pick it up and they had put a Schengen visa on it, this works to travel all of europe without hassels or problems.
Hope this helps.