Your husband might be surprised how many written records there were. I hate to mention the 's' word, but when you get back that far, people were a commodity and were documented. Before that point is reached, there is civil registration from c1880.
As for Africa, I think that most of the people who ended up in the West Indies were taken from the west coast of Africa, Gambia, Nigeria, Benin, but there will be plenty of info on this if you google.
As to where you start, I would suggest you get a large piece of paper and write down/draw out everything that your husband knows about his family and then see if anyone from the previous generation can fill in any of the gaps and go from there.