While this morsel of history has been portrayed in pop culture over the decades, including in last year’s “Gaslit,” it was not until now, half a century after the fact, that the men who planned the bugging of the Democratic National Committee headquarters and didn’t quite pull it off have been deemed worthy of their own miniseries. So we come to “White House Plumbers,” a tale in five parts, premiering Monday on HBO.

Nominally based on the 2009 memoir “Integrity: Good People, Bad Choices, and Life Lessons from the White House,” by Egil “Bud” Krogh, head of Richard Nixon’s Special Investigation Unit — called the Plumbers, because its purpose was to stop leaks — the series focuses on the misadventures of brothers-in-abbreviated-first-names, former CIA operative E. Howard Hunt (Woody Harrelson) and ex-FBI agent G. Gordon Liddy (Justin Theroux). Krogh (Rich Sommer) gave them their first job, overseeing the burglary of the office of the psychiatrist of the Pentagon Papers leaker, Daniel Ellsberg, on a fruitless search for damaging information. The Watergate gig — the least extreme of Liddy’s ideas for messing with the opposition — famously followed.

Even before starting to watch, one would expect a comedy, and that “White House Plumbers” comes from writers Alex Gregory and Peter Huyck and director David Mandel, who all worked on HBO’s “Veep,” only doubles that expectation. And so it is. When Liddy and Hunt go to reconnoiter the psychiatrist’s office, they wear terrible wigs by way of disguise. The bungling of the break-in — there was more than one, trying to get it right — borders on farce. (Even Nixon, on his infamous tapes, can be heard calling it a “comedy of errors.”)

With his greasepaint-black hair and mustache and his pulp-fiction posturing, Liddy was in life already three-quarters of the way to a caricature. Even those with a passing knowledge of him are liable to know that he ate a rat to cure himself of a childhood fear and would hold his hand in a flame to demonstrate how tough he was. (You can find him discussing these things with David Letterman.)

Indeed, Liddy’s whole adult life can seem like one long act of overcompensation, and his on-the-record statements, merely translated to the screen — including his readiness to assassinate, and if necessary, to be assassinated, asking only for “a clean head shot” — do come off as bizarrely humorous. Theroux invests his speech with a psychotic precision that doesn’t resemble the real Liddy, yet it gets the point across. Nothing in Hunt’s biography, on the other hand, seems especially humorous, but Harrelson plays him at medium-high boil, with a thrusting chin and gravelly voice and often in some sort of emotional extremity. Together, they enact an on-again, off-again battling bromance — a temperamentally mismatched but ideologically compatible couple, as in countless buddy-cop flicks, with the difference being that they’re failures.

Lena Headey plays Dorothy Hunt, the spouse of E. Howard Hunt, in “White House Plumbers.”

(Phil Caruso / HBO)

“Veep” is a certified great comedy, but it’s one thing to create a show about Washington monkeyshines using original characters in original stories and another to make it with some necessary regard for real events and people, especially when, in Hunt’s case, their life was touched with tragedy. (I would be more specific, but it feels like a spoiler.) As a result,”White House Plumbers” suffers from a kind of tonal confusion that keeps it from being wholly successful either as comedy or, as well-researched as it is — you can find the oddest of these events in the voluminous record — as believable history.

In the role of Dorothy Hunt, who would play a major role in this story, Lena Headey — perhaps best known as Cersei Lannister on “Game of Thrones” — seems to be acting in a different series altogether. As Hunt’s children, Zoe Levin (haunted Lisa), Liam James (adoring Saint John), Kiernan Shipka (model daughter Kevan) and Tre Ryder (young and innocent David), similarly inhabit a family drama tonally distinct from the satirical political story. (The Liddy children, by contrast, appear only briefly, lined up on the stairs like the Von Trapps to greet the Hunts at a dinner party, before being sent back to their rooms and out of the series. At which point, Liddy proceeds to entertain his guests with an LP of Hitler’s speeches — played loud — while Hunt begs for some jazz.)

That’s not to say that “White House Plumbers” isn’t interesting or watchable, or sometimes as funny as it wants to be; there’s too much talent behind and in front of the camera for that to be the case. There’s some fine bumbling in the burglary scenes. The production is first-rate, the period work never rings false, crowd scenes are not threadbare, and choice D.C. locations keep the weirdness real. A varied supporting cast includes Ike Barinholtz as Watergate conspirator Jeb Magruder; Gary Cole as Mark Felt, later Deep Throat; F. Murray Abraham as Judge John Sirica; Tony Plana, as Eugenio “Muscolito” Martinez, is the most recognizable of the Cuban burglars; Toby Huss, quietly stealing scenes as burglar James McCord; and Kathleen Turner in a wild, coarse turn as scandal-embroiled lobbyist Dita Beard.

And there are elements, of course, that speak to our present condition. Even though it came back to bite him, Nixon’s willingness to break the law — and ordering others to break it — does seem to mark the beginning of a win-by-any-means age. At the same time, the archival clips that punctuate the series indicate a markedly different time, when the news was not the business of pundits and a paranoid president’s own party could convince him it would be best for the country if he let someone else drive. It almost makes you nostalgic.