Rob Lowe as Father Jude Sutton and Gaia Scodellaro as Sister Celine in “You, Me and the Apocalypse” on NBC. (Ed Miller/WTTV Productions Limited)

A comet measuring eight miles across is going to collide with Earth in 34 days and kill us all, which, I assume, will deal yet another setback to the traditional television industry. People are panicked, desperate. News of an impending doomsday has NBC doing weird things, such as making and broadcasting semi-serious dramedies with the British.

The result, a joint production with U.K.-based Sky 1 called “You, Me and the Apocalypse” (premiering Thursday), is a fun but slow-going experiment in end-of-the-world gallows humor. If you can restrain yourself from screaming “What is this?” at the screen during the first episode, the show does unspool an engaging (if convoluted and only sometimes funny) story to share about a very disparate group of people who are each connected to the impending event.

Rob Lowe co-stars as Father Jude, a self-centered Vatican priest who holds the title of “devil’s advocate,” tasked with disproving miraculous claims attributed to candidates for sainthood — a job that suits his cynical, snide nature. With the comet approaching, his superiors reassign him and his assistant, Sister Celine (Gaia Scodellaro), to investigate claims of new messiahs whose presence would precede a biblical apocalypse.

“You, Me and the Apocalypse” simultaneously launches into a dizzying number of global subplots — so many “meanwhiles” that it then tediously tries to knit together in the remaining nine episodes. Jenna Fischer (“The Office”) plays Rhonda, a librarian doing time in a New Mexico prison for hacking into the National Security Agency’s computers. (In fact, she’s covering for her teenage son.) News of the comet leads to an inmate riot in which Rhonda escapes with a white supremacist, Leanne, played by Megan Mullally with bottle-blond tresses, buckteeth and a swastika forehead tattoo. (Mullally might be the only reason to stick with the show long enough to figure out what’s going on.)

In London, a bank manager, Jamie (Mathew Baynton), is arrested for computer hacking, which leads him to discover that he has a twin brother, Ariel, who leads a band of online revolutionaries called Deus Ex Machina. At the White House, a national security adviser named Scotty (Kyle Soller) suggests a plan that will at least stave off social chaos while the world’s scientists convene to come up with a plan to prevent the collision — which seems unlikely.

Only when we learn that Rhonda (see above) is Scotty’s sister, and that her son has been kidnapped by the Deus Ex Machina hackers, do these stories show the remotest hint of coming together — and miles of deliberate confusion ahead before they really congeal. Creator Iain Hollands has given “You, Me and the Apocalypse” a sort of intellectual larkiness to the characters’ rapport that plays like zero-calorie “Doctor Who” episodes.

It doesn’t strike me as the sleeper hit that will save network TV from its impending doom, but it is a show that clearly uses its noggin, even when the action drags. It’s certainly something different from the usual prime-time fare, and that, it seems, is the key to the medium’s survival.

You, Me and the Apocalypse (one hour) premieres Thursday at 8 p.m. on NBC.