Michael is the son of infamous mafia boss Fat Tony, but he does not wish to follow in his father's footsteps and go into the family business of "waste management". He has a passion for cooking and is a great chef. His mother died when he was younger and he has no siblings.
His father, Fat Tony was once put in a hospital by rival gangs and Michael was offered to take over the mafia for a while. He did not want that and Homer and Bart took over the mafia instead although later he willingly poisoned the gang that had attacked his father. It is unknown what happens to Michael after his father's death, though he may now be in the custody of the new Fat Tony.