Mussomeli's grandparents on both sides of the family immigrated to America from Sicily around the turn of the 19th century. Mussomeli was born in New York City on May 26, 1952. His father, Mariano Mussomeli, was an officer in the United States Army and served in both World War II and the Korean War. As such, Joseph moved around the US somewhat in his youth, and also lived for some time in Germany.