Father = Mikkos Cassadine
Alexis was the product of an affair between Mikkos and an opera singer. Mikkos is now deceased, but I have no idea how or when this happened.

Mother = Kristen Bergman (I think!)
Kristen was a very famous opera singer. She had an affair with Mikkos, and as a result Alexis was born. Kristen kept Alexis with her up until Helena found out about the affair and the child, and had Kristen killed.

Stepmother = Helena Cassadine
Killed her husband's mistress, but agreed to raise Alexis as a cousin of the Cassadine's. Helena has tortured Alexis and many other Port Charles residents in past years.

Siblings = Stefan and Stavros Cassadine
Stavros was killed by Luke Spencer years ago, but Stefan is still alive. He lives on an island called Spoon Island, with his son Nikolas.

Nephew = Nikolas Cassadine
Nikolas and Alexis occasionally get along, but for the most part, Nikolas is wary of his Aunt. Nikolas lives in a cottage that formerly belonged to Brenda Barrett.

Best Buddy and Boyfriend = Ned Ashton
Ned and Alexis have been dating for some tome now. They have recently come to the conclusion that they are in love with each other, and hopefully more will come to this romance.