Mother Battle-Axe is Miss Battle-Axe's mother. She seems to think her daughter, Miss Battle-Axe, cheats Horrid Henry. She likes Henry and thinks he is a good boy because when she is around, Henry is as nice as pie. She makes brief appearances throughout several episodes.
It's unknown about Mr. Battle-Axe (Miss Battle-Axe's father) since he has never been mentioned, it's possible he is deceased, or away from the Battle-Axe family.