I'm cuban and I went to Ecuador in 2012,from there I crossed until i arrived in mexico US border and well we cuban dont actually apply for refugee status but for the Cuban Adjustment act...and for the person who said''did he came swimming?'' yes my friend some cubans arrive swimming in miami beach(i tried once) obviously not straight from cuba but when you are close to the beach lol(look up for cuban rafters on google or youtube that will tell you something...)
now,for the person asking,,Your husband has to wait the full year nd 1 day to apply for his Permanent Resident green card(which takes 5 or 6 months) and then he can go to canada no problem without a visa...That would be the best choice since most likely your application will go to Ottawa since HE LIVES IN USA AND is a permanent resident...
Without waiting the full year,CIC will take a long time to process your app because first of all he is not yet a FULL PERMANENT RESIDENT OF USA and if they sent his app to Cuba he will have to go there for the interview(and i dont know how exactly he left so,he might not be allowed to come back) If and only IF he got lucky and CIC sent his app to Ottawa he might either have the interview in LA or just receive the COPR...
Most Cubans go to Miami because thats the best place for cubans to be,,,youre welcomed there,,and you have the biggest community in the world(at least cuban)....Most cubans who married Canadians(in cuba) was only to cross the border Can-USA and go to MIami,,,so CIC might look different at your app since He is already free,,already in USA,,why would he go to canada if he didnt love you? there is nothing for cubans in Canada(and we dont love winter that much lol) again,,Cubans go to Canada to LEAVE TO USA,,not the other way around so,CIC wont scrutinize your ap as if he was in Cuba....
There is still another way for you to bring him right away,,he would be with you in Canada legally in two weeks,,,,tell me if you need more info on this,,I suggest you to tell him to wait until he gets his green card(which i did and now im married, my case was exactly like his,,I waited and then came back to cuba and brought all my wifes family and had the wedding there and now im in canada waiting for the process here)..