Honestly, this is one of Jim Henson's finest hours--the ultimate crossover of all Muppet universes, with a cameo by Jim at the end that still chokes me up. Shame it's not readily available, though you can find it on YouTube in the infamous "dying baby" cut. But you should watch it anyway.
Reposted from
Sesame Street History
OTD in Sesame Street history, 12/16/87, A Muppet Family Christmas premiered for the first time! This special featured the Muppets, the Sesame Street cast, the Fraggles, and Henson himself.
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https://youtu.be/Bi9qSKZuvC4?t=2827
And then. It just goes on with the Christmas programming?! Ugh. Immaculate.
This version isn’t pristine, but it’s about as complete as we’re ever going to get.
https://youtu.be/Bi9qSKZuvC4?t=2827
It almost reminds me of this classic snafu.
https://youtu.be/fYUhHgs80bg?si=joQEvHFiLq87Mvxq
https://youtu.be/Bi9qSKZuvC4?t=2827
https://www.youtube.com/watch?v=Ovb56dlcodE
https://muppet.fandom.com/wiki/A_Muppet_Family_Christmas?useskin=fandomdesktop#Edits
The most obscure omission is probably Fozzie and Elmo lighting the Christmas tree together. So if the version you find online has that, chances are it's complete.
These re-edits and chops to specials drive me insane.
I just want the definitive version!
47:30 Runtime is the longest version I've seen, and I've been tracking it down online for years.
https://www.youtube.com/watch?v=Bi9qSKZuvC4
https://youtu.be/Bi9qSKZuvC4?t=2827
Elmo popping up in a few silent background appearances bought some time early on. It’s hard to explain to a toddler why Elmo and Abby aren’t in a 1987 special.