You can find a complete description of all the characters here: http://www.enotes.com/lie-down-qn, but briefly we have Milton Loftis, Peyton, and Helen. These three are the main characters in the story. Milton is the father and central voice of the novel. He tries desperately to keep the family together. He is sensitive but weak, without enough will power to make the right decisions and avoid tragedy. He is overly cautious and selfish.
Helen (the wife) is cold, manipulative, intolerant and obsessively jealous. She is cruel, and clearly pathological in her coldness.
Peyton (the daughter) is caught in the middle between the two. She is beautiful and intelligent, proud and independent. She also has taken from her parents and becomes selfish (like her father) and incapable of love (like her mother).
The other characters in the novel are inconsequential and serve more to move the story forward than as round characters.