New parents Miles and Nina have just bought a brownstone in a not-quite-there-yet Brooklyn neighborhood. The place is completely unrenovated, and since the birth of their daughter Hannah, their marriage has become a bit of a fixer-upper, too.

Thus begins “Satellites,” Diana Son’s patient, rigorous, quietly affecting account of two people in love struggling to obey the rules they have created for themselves. She poses several provocative questions about self-definition and familial obligations, and even if these questions aren’t resolved sufficiently by the end, Ms. Son and her two superb leads see to it that they are asked with all the complexity they deserve.

Although Nina (Sandra Oh of “Sideways” and “Grey’s Anatomy” fame) and Miles (Kevin Carroll) profess delight at having a biracial child – she’s Korean, he is black but was raised by a white family – the mounting tensions between them have plenty to do with forging a racial identity for their new family. “Dad can break out the family albums going back seven generations,” Miles says, “but when she looks at those people in the photographs, she won’t see herself.”

Their problems go well beyond those of skin color. Miles has been laid off from his dot-com job, his scheming brother Eric (Clarke Thorell) has shown up from Malaysia uninvited, Nina’s two-person architectural firm is scrambling to finish a major proposal, her C-section operation still hurts, and they arguably can’t afford their new home. (Mark Wendland’s masterful set, a jigsaw puzzle of distressed walls and cavernous rooms, would tempt many a New Yorker to put down an imprudently large down payment.) And then someone throws a rock through their 80-inch picture window. Or did the truly shattering blow come six weeks earlier, in the form of a baby girl with “chocolate skin and almond eyes”?

As with her excellent 1998 play “Stop Kiss,” which also featured Ms. Oh and Mr. Carroll, Ms. Son shows a sharp ear for the conversational details that nudge a relationship forward or backward. She and director Michael Greif grasp the ever-changing ramifications of how two people in love disagree (and the affection between Nina and Miles is never in question); more impressive is their understanding of how these disagreements change when other people are in the room.

The strains of parenthood are more visibly apparent on Nina. She begins lactating at the sound of Hannah’s cries, and she struggles to balance her demanding career with what she calls “this feral, this animal drive to take care of my daughter.” Her marriage, meanwhile, threatens to fall into a distant third place, and Miles isn’t helping matters by refusing to hold Hannah and by entering into a questionable business scheme with Eric.

Chemistry can be tough to establish when two characters are at each other’s throats more or less from the beginning, but Ms. Oh and Mr. Carroll display a lived-in comfort with Ms. Son’s chatty dialogue. Ms. Oh trades on her well honed persona as a potty-mouthed cynic at first but quickly expands the role; Nina is an ambitious, conflicted, loving, complicated woman, and Ms. Oh navigates these emotions with a nimble versatility.

And Mr. Carroll (best known as the doomed Christian ballplayer in “Take Me Out”) emanates a rare quality on stage, that of a somewhat effortful decency. Ms. Oh’s strengths manifest themselves in the way Nina’s personality changes slowly, almost imperceptibly over the course of the play; Mr. Carroll’s strengths manifest themselves in the way Miles changes with each individual interaction. He has assimilated masterfully into every role asked of him – except that of a father.

Miles and Nina both have tenuous connections to their roots: He was the abandoned son of a heroin addict, while she grew up as the only Korean girl in her Midwestern town. Hannah’s birth triggers a series of tentative, potentially regrettable steps on their part to sort out their own cultural hang-ups. Nina hires a Korean nanny, Mrs. Chae (Satya Lee), hoping that Hannah will learn to speak Korean, while Miles strikes up a wary acquaintance with their neighbor Reggie (Ron Cephas Jones), a smooth-talking layabout who’s seen the area during considerably worse times.

Ms. Son teeters on the brink of condescension with the earthy, syntax-mangling “ethnicisms” of both Ms. Chae and Reggie, although Ms. Lee and the reliably amusing Mr. Jones help keep the characters honest. However, the role of Nina’s business partner Kit, who takes turns wittily flirting with Eric and grumbling about Nina’s lack of focus, is too thinly drawn to inspire much beyond garden-variety comic relief from Johanna Day.

The percolating emotions between Miles and Nina, which flare up in small but telling ways throughout, reach a breaking point in the last two scenes, as the fault lines of their marriage give way to an explosion of banked regrets and resentments. It’s only at this point that the character of Miles comes into full relief, and the fights pave the way for a beautiful final image (another example of Mr. Wendland’s gorgeously detailed work) that is both sobering and comforting.

It is also perhaps a bit unearned – not every accusation can be unsaid that easily. But Ms. Son gambles on the fact that this central relationship has been solidified to the point where audiences will give Nina and Miles the benefit of the doubt out of sheer empathy. Thanks in no small part to Ms. Oh and Mr. Carroll, her gamble pays off. The Korean-speaking nanny may be gone, but these three will learn to speak the same language. That’s what families do.

Until July 9 (425 Lafayette Street at Astor Place, 212-260-2400).