Hi.
It may be more common than you think for people to feel that family members are one way behind closed doors, but present a different face to the public. Dr. Sharon Budd, who specializes in child and adolescent psychology, says this perception is quite keen among adolescents, who begin to scrutinize their parents' behavior more closely.
Question is what to do about your dad? Dr. Budd believes that family therapy might be helpful in this case, but your father may be quite resistant to the idea. If you think the suggestion would do more harm than good, perhaps you could try talking to your mother about all of this. It seems, from your description, that she may feel equally bullied, but she may have more pull than you do. Try explaining how his behavior affects you and ask her if she can talk to him on your behalf.
Truth be told, there may be little you can do about your father's behavior, if he doesn't see the need to change, but taking care of yourself is essential. As you go through this, try to get some support in coping with your stressful household. Speak with an adult you trust--a school counselor would be a good start. He or she would be able to delve much more deeply into these issues than I ever could, and give you some suggestions based on the information you provide.