Bad Parents are the type of villains who are father or mother to the hero or heroine. Many of these evildoers qualify as Abusers and Disciplinarians, as they may abuse their children (psychologically, emotionally, physically or perhaps even worse) either because they do not obey or simply by pure sadism - though not all villainous parents maltreat their children.
In other cases parents (father or mother) at first they seem to be caring and loving until when hero or heroine discovers their dark secret eg. from past, when murdered someone or was criminal. Often it happens, that hero/heroine's father is a villain, while mother is heroine, sometimes the opposite happens.
Also villains have their own children which cares about them and they help their parents, eg. crime lords want appoint a son for the successor. Some of the children of villains are loyal to their parents, some other doesn't want to follow in his footsteps and become evil.
On the other hand, being a parent can stand as a redeeming quality because some of these villains may reform themselves in order to protect and take care of their children, or saving them from others evil-doers.