Affluent, satisfied families are to modern plays what plate-glass windows are to action movies. The moment you see one, you can count the minutes before it gets smashed to bits.

The latest wreckage can be found in “A Naked Girl on the Appian Way,” Richard Greenberg’s pleasurable and surprisingly even-keeled new comedy. As soon as the curtain rises on the impeccable Hamptons home of Bess and Jeffrey Lapin (Jill Clayburgh and Richard Thomas), you can practically hear the time bomb ticking.

Bess is a celebrated lifestyle guru – her last book featured an entire chapter on edamame – while Jeffrey is a tycoon who has shifted his energies to writing about the humanizing effect of art on business. He relies on Bess a bit too much (“If you hadn’t married me, you would have had to hire me,” she patiently tells him after finding his inhaler yet again), but the two are so self-effacingly secure, so damn content, that it’s hard not to root for the disaster.

Mr. Greenberg, who has emerged as our theater’s pre-eminent semi-serious comedy writer, acknowledges this urge right off the bat. At the sight of Bess making a predictably perfect 49-ingredient salad, Jeffrey gently goads her, “Do you wish there were doubt? Do you miss the possibilities of drama the occasional failure provides?” Not to worry, Jeffrey.

The salad is part of a meal being prepared for a family reunion. Their three gorgeous adopted children – a put-upon Japanese son, a slightly dim-witted German son, and a scholarly Dominican daughter – are about to join them to celebrate the return of the latter two after 17 months in Europe. But Mr. Greenberg and director Doug Hughes introduce teasing hints of some slightly amiss occurrences while Thad (Matthew Morrison) and Juliet (Susan Kelechi Watson) were abroad. (The play’s title stems from a totemic image that the two saw on their travels.) They return from their “wanderjahr,” as it’s repeatedly called, with news that throws the family’s equilibrium into a tailspin.

Without giving too much away, the dirty secret involves sex. “Naked Girl” is the latest in a growing trend of dramedies about modern families grappling with sexual transgression. The prime example is Edward Albee’s “The Goat,” but even closer parallels can be found in Nicky Silver’s underrated 2004 play “Beautiful Child.” In all three cases, the limits of tolerance within an ostensibly functional family are tested in the face of deviance (bestiality and pedophilia in the previous two cases).

But something interesting happens here, or doesn’t happen; Mr. Greenberg lowers the stakes. He doesn’t describe any actual crimes – unlike Messrs. Albee or Silver – nor do we find ourselves in “American Beauty” territory. The big news is treated less as a sign of the moral rot that has always lurked underneath than as a problem that needs to be discussed and resolved. The parents’ initial responses are so equable – “We have well-honed techniques of denial,” Bess explains almost apologetically – that Mr. Greenberg is compelled to boost the indignation quotient by adding an additional shocker two-thirds of the way in.

A prerequisite of these plays is the dis senter within the ranks – the furious family member. This time it’s Bill (James Yaegashi), the older brother who didn’t get to go to Europe. His tirades, drenched with self-pity – he even uses the fact that he went to Harvard (Goucher was his first choice) as ammunition – are hugely entertaining. Mr. Yaegashi conveys Bill’s disapproval with withering intelligence.

Mr. Morrison is equally captivating as Bill’s polar opposite, a dim-bulb golden boy who sees only the best in everything and everyone. Mr. Hughes’s nimble direction contrasts the two brothers beautifully: When Bill tries to tell Thad that he’s always hated him, Thad laughs it off as filial banter and puts him in an adoring headlock. (Among the many assets of John Lee Beatty’s handsome set is its durability: Mr. Morrison bounds over every surface like a puppy whose owner has just come home.)

The ridiculously prolific Mr. Greenberg (three more new plays are debuting this year, not to mention a Broadway revival of his “Three Days of Rain”) shares with Tom Stoppard and Michael Frayn a gift for sparkling dialogue – and a weakness for parceling it out to every character regardless of whether they would or should talk like that. Take this comment from one of the kids:

We were in Europe and suddenly there were no borders. Right: Europe is gazillions of borders but it was like, you’d cross one and it was terra nova but in a way not – because it’s not like the country didn’t exist before; it was just waiting for you to enter it.

That’s a crisp, well-oiled, terrific piece of dialogue – except that it comes from Thad, the dummy of the three children. The level of erudition ratchets up from there: Henry James, Jessica Mitford, and even the historian Barbara Tuchman all pop up as punch lines.

This love for bright, shiny dialogue is nearly fatal early on. Mr. Thomas and Ms. Clayburgh deliver exposition for the first 20 minutes, but Mr. Hughes somehow manages to give some semi-plausible fluidity to the scene. Ms. Clayburgh has that mega-salad to keep her busy, while Mr. Thomas roams around the set looking for things. They get a little help from the riotous Ann Guilbert as Sadie, the elderly feminist next door who periodically meanders through the Lapin home muttering expletives. (To her surprise, Sadie’s son found her book “Against Motherhood” objectionable. “And to think: With the exception of a mother’s love, he had every advantage.”) As much fun as Ms. Guilbert is, the truth-telling old potty mouth doesn’t exactly qualify as pioneering writing; “The Golden Girls” comes to mind, as does one of Mr. Greenberg’s first major works, “Eastern Standard.”

Sadie and her daughter-in-law (an underused Leslie Ayvazian) resurface near the end, largely to introduce a mini-bombshell involving Bess. In the grand scheme of things, the piece of information is not terribly interesting. It exists largely to give Mr. Thomas and Ms. Clayburgh something that isn’t purely reactive: After more than an hour of laying plot points at the feet of his two above-the-title stars, Mr. Greenberg basically hands them a turn in the spotlight.

Which is not to say the two don’t find their laughs: Bess’s aforementioned gift for denial lends itself to Ms. Clayburgh’s equally well-honed blend of dither and discipline, while Mr. Thomas brings a genial energy to his earnest dad bending over backward to maintain a “disinterested attitude.” But just as the parents are a bit at a loss until the kids arrive, Mr. Greenberg seems content to let his stars fend for themselves.

The affability embodied by Jeffrey carries through even the play’s most turgid bits. Sadie’s reliably hostile appraisal of the Lapin parents proves useful: “At one time in my life you two represented everything I was hoping to destroy. [Pause.] That was then, this is now. I’d love another scone.” After all the wailing and teeth-gnashing, Mr. Greenberg’s mostly unflappable brood proves just as accommodating. Anyone looking for something more bitter, more bruising, than a scone may leave “A Naked Girl on the Appian Way” hungry. But it sure is tasty while you’re there.

Until December 4 (227 W. 42nd Street, between Seventh and Eighth Avenues, 212-719-1300).