It's a Miserable Life
On Christmas Eve, the citizens of Highland (including Principal McVicker, Stewart's parents, Van Driessen, and Tom Anderson) pray to God for the deaths of Beavis and Butt-head. In the heavens, noting there is no other recourse left, God assigns Charlie, the duo's guardian angel who had not yet gotten through to them, to take away their lives.
After leaving the house, disgusted over television's usual glut of Christmas programming, Beavis and Butt-head wander outside in the hope of scoring. They're a little confused about why nobody else is outside, even after Finley at the Maxi Mart informs them that it's Christmas Eve. Their unachievable task ends up at an unstable bridge over a active, flowing river, where they start messing around in a way that could knock them off the bridge - it is then that Charlie manifests himself, bringing up chill winds to finish the job they started. After that only causes the duo to leave ("cold sucks!"), Charlie tries to get them to come back... only to fall off the bridge himself.
Charlie climbs out of the river and converses with B&B in order to convince them to commit suicide "for the good of all mankind". Failing at that, Charlie then sends Butt-head to an alternate universe in which he was never born, in an attempt to convince him that the world would be better off without him.
Highland is a changed place. A festive Christmas celebration is happening in the town square; without the negativity of Butt-head, Charlie argues, people would be happier. Mr. Anderson is anchoring a Christmas light display, which Charlie notes would not have been possible with Butt-head's routine destruction of Anderson's front yard (Butt-head manages to blow all the lights up by tripping over a cable). Burger World is full of customers, since Butt-head didn't drive them away. Of the utmost importance to this website, Charlie and Butt-head visit Highland High, where a joyful, fully-haired Principal McVicker is leading a choir consisting of Highland students, including Daria.
Choir (feat. Daria): Tis the season to be jolly, falalalala, lalalala!
As Daria, grinning the whole time, holds the hands of a boyfriend, Charlie notes to Butt-head:
Charlie: And you weren't there to destroy Daria's image of boys.
Butt-head wants to see what happened to Beavis, who owes him a dollar, and is shown the most horrific of alternate realities: Beavis is happy and well-adjusted and volunteering to help people at the homeless center. With his friend Stewart. And because Butt-head wasn't around, Stewart has self esteem. A sickened Butt-head tries to drag Beavis away but is prevented, and is distraught that the guy doesn't know what a bunghole is. ("You're a bunghole, bunghole!")
After being returned to his own timeline, Butt-head decides not to jump because Highland sucks without him around. Charlie chases after him, only to slip off the bridge, fall in the river, and get dragged away while the duo laugh.
This figure goes unnamed in the episode but is a recurring background character, Martin, from Daria's classes. His winter gear covers up his usual hair and Punisher T-shirt. often shown in a Punisher T-shirt. (He went unnamed until a 2011 episode.)
Martin only interacted with Daria once on the show, talking with her in the background in "Substitute". But in another world, who knows...
Beavis and Butt-head had a "sliding timescale" approach to continuity: they remain fifteen forever. Daria had chronological progression though. So while it's fine for Beavis & Butt-head to have had this Christmas story, another Christmas story during the same episode set on the exact same days, and two comics (one with Daria) set during Christmas and all of them coming after a lot of other B&B stories with Daria in, it does cause chronological issues for Daria.
The easiest way around this is to assume Beavis and Butt-head is out of chronological order: her Christmas stories with them occur before the other stories which were produced before. This does mean that Butt-head destroyed Daria's interest in boys extremely rapidly, but in fanon it's assumed that Daria went to the same junior high and/or elementary schools as them; Butt-head is also a very visible and dominant personality, quite able to make a (bad) impression.
This still leaves us with one issue, that Principal McVicker has lost his hair and sanity in just over three months, but we'll write that off as It's Only A Cartoon before we all go mad.
The buttmunches watch a brief clip of It's a Wonderful Life, just so we get the homage.
Butt-head destroying Daria's interest with boys links up disturbingly well with the events of their fourth comic...
Van Driessen praying for their death is abnormal for him; he cites his reason as concern for "what if they might breed?".
This is an explicit statement that not only does the supernatural exist in canon, so does a version of the Christian God and His Heaven, and the non-Biblical concept of guardian angels. This puts an interesting spin on Daria episode "Groped by an Angel"...
As has been noted by Kristen Bealer, this is a highly significant AU: a happy, well-adjusted Daria with emotional ties would be far less likely to end up in the self-esteem class and meet Jane, or indeed have so many snarky adventures. Which means we should be glad Butt-head was born after all!
While Daria's demeanor and view of life is presumably greatly changed from the standard universe, Charlie only comments on how Daria's love life is affected.
Miserable Life and fanfiction
"Coming of Age" by Deep Metal has a chapter where Charlie returns and shows Beavis a world where he had the opportunity to become a good, competent young man. "A Well-Adjusted World" by Charles RB shows the end-result of Daria being well-adjusted and nice.
Several fanfics make use of Martin.