Their mothers never appear, but they do apparently have a mother each, and aren’t brothers. Look under “Beavis’s Parents”
The old disclaimer:
“Beavis and Butt-Head are not real. They are stupid cartoon people completely made up by this Texas guy whom we hardly even know. Beavis and Butt-Head are dumb, crude, thoughtless, ugly, sexist, self-destructive fools. But for some reason, the little weinerheads make us laugh.”
In the episode It’s a Miserable Life, where Butt-head’s guardian angel shows Butt-head what life would be like without him ever being born, we see Beavis volunteering at a soup kitchen with Stuart bossing him around.