You have really chosen the one of the trickiest possible combinations for your travel plans!
There are some scheduled airlines flying both to HAV and the US (e.g. IB, AF), but I doubt that open-jaw routings are possible e.g. for a trip to HAV and back from the US.
On November 1, 2001, Continental Airlines started twenty weekly charter flights from the United States to Cuba, using Boeing 737 aircraft, with flights
originating primarily from Miami, one of the U.S. approved gateway cities for travel to and from Cuba. The other U.S. cities with direct flights to Cuba are
Los Angeles and New York city.
The charters are operated by Gulfstream International Airlines and the Continental Connection. Only people with permission from the United States
government may legally take the charter flights. It is essential to know what the law is regarding legal visits to Cuba.
Americans visiting Cuba without licenses should know that U.S. immigrations forms for returning travelers ask what countries they have visited. If an
Immigration or U.S.Customs officer asks you directly if you have visited Cuba note that it is a federal offense to not tell the truth, at which point you may
receive a lecture, citation, close scrutiny, or whatever the dictates are, including monetary fines. However, it is in no way a scary or intimidating
procedure as long as you have not tried to bring back any illegal contraband.
Homer: Facts are meaningless. You could use facts to prove anything that's even remotely true!