Eddy's Parents are well, Eddy's Parents.
Eddy's Mom is...well, the mother of Eddy and his brother. She has been mentioned in the show numerous times, but is never fully seen. However, her arm is visible in the episode "Smile For The Ed". She promised to Eddy that she would give him the key to his brother's room if his school photo is nice for once. She once cleaned out Eddy's room in "The Luck of the Ed."
Eddy's Dad is obviously Eddy's and Eddy's Brother's father. He only has one appearance, though it is only in the form of his large, hairy, arm dragging Eddy away in the episode "Mission Ed-Possible." He is one of the few Adults (ther than Ed’s or Eddy’s mom) to have their presence acknowledged in the series. As the shot shows, he wears a watch and a ring on his middle finger (They only have 4 fingers). In the episode "Ed, Ed and Away" Eddy makes a comment that suggests that his dad may be an auto salesman. Eddy's Dad obviously got angry at Eddy for the bad report card (we can imagine how much big trouble Eddy was in) It is unknown what the punishment was. It is unknown if Eddy's Dad knows about the history of Eddy's family, since Eddy himself hadn't known his family had set up place where Peach Creek later came to be. So it could be assumed that either he didn't know about it (most likely), or he just didn't or even forgot to tell Eddy about it (also likely). Also, Eddy's Dad will not tolerate bad grades from his son. In the episode "Keeping up with the Eds," it is revealed that Eddy's Dad uses a fertilizer that can make mushrooms grow anywhere, including the proven bottom of shoes. It is unknown why he only gets him (and possibly his other son) clothes every Christmas. He possibly gets angry easy.