In 2006, Nell Freudenberger was on a plane to Rochester, upstate New York, when she got chatting to a Bangladeshi woman and her white American fiance. The couple, she learned, had met several months earlier on an internet marriage site, and were travelling to Rochester to start their life together. Freudenberger was fascinated by the unusual nature of their relationship, the way it blended aspects of an arranged marriage with "this very new… [online] form of courtship". And she was struck, too, by the woman's bravery. "For a Muslim woman, I knew her choice was almost unheard of. What had given her the courage to leave behind everything she knew for a life she could barely imagine?"

Freudenberger sensed that it might be possible to put her story to fictional use. "When I met her, I had a feeling I can't explain when I met her," she says, "as if we were already much more intimate than an hour-long plane trip could justify."

Six years later, that chance encounter has come to fruition in Freudenberger's highly impressive second novel, The Newlyweds. Written with the approval of Farah, her plane companion (the pair became friends, and even travelled to Bangladesh together), it tells the story of Amina, a young woman who leaves her village in Bangladesh to marry George Stillman, a plodding engineer from Rochester, after meeting him on AsianEuro.com. With great sensitivity and psychological subtlety, Freudenberger charts the misunderstandings and disappointments – and occasional rewards – experienced by the couple in their first few years together.

Freudenberger, who is 37, was already feted by her late 20s, when the New Yorker (where she used to work) began publishing her stories, and she was included in Granta's 2007 "Best young American novelists" issue. Now The Newlyweds, which was published in America earlier this summer, is earning rave reviews.

I meet Freudenberger in a crowded cafe in Park Slope, the pushchair-filled Brooklyn neighbourhood where she lives with her husband, an architect, and their two small children. Amid the din, Freudenberger is a serene presence. She speaks in a quick, even voice that at times threatens to become a mumble. I begin by asking her about her longstanding interest in cultural collision. Many of the stories in her critically acclaimed 2003 collection, Lucky Girls, featured American women travelling in Asia, while her first novel, The Dissidents (2006), was about a Chinese performance artist who spends a year in LA. What, I wonder, explains this outward-looking tendency? After all, it's not something for which American writers are renowned, apart from those (such as Jhumpa Lahiri or Téa Obreht) with backgrounds in other cultures.

"I started writing about other places just because I happened to be there," Freudenberger says. (In her early 20s she had spells living in Thailand, India and China.) "But three books into it, there has to be more of a reason than that. I think, for me, it's a way of writing about being American. I find it hard to get into doing that without an outsider's point of view."

The Newlyweds, she says, was a difficult book to get going with, largely because she initially felt the need for "an American perspective" to counterbalance Amina's. Her first try-out was a story published in Granta, Where East Meets West, which describes a bigoted old woman's reaction to a young Bangladeshi moving in next door. When it came to the novel, she experimented with telling the story from the point of view of various American characters, but couldn't make anything work. "It got really frustrating. At one point my editor said, 'Just keep going with Amina and see what happens.' And that turned out to be the answer."

Wasn't Freudenberger anxious about appropriating her friend's experiences, even though it was just the outline of her situation that she borrowed, not the story of her marriage? "Yes. I always worry about my interest in material that isn't my own." She points out that one of the people Amina encounters in Rochester, a cousin of George's named Kim, functions as a repository for this fear. Kim is a westerner who embraces all things eastern: she's into yoga, wears ethnic clothing and had an Indian boyfriend. Naturally, she befriends George's new wife too, but her interest in Amina – and indeed, in all things subcontinental – is shown to be shallow and self-serving, an unflattering reverse image of Amina's desire to establish a life in the west.

I ask Freudenberger what books she has liked recently: she has been rereading George Eliot, as well as reading Rosemary Ashton's "definitive" Eliot biography. She begins describing Eliot's unconventionality – her decision not to have children, her "sinful" relationship with George Lewes – and it's almost as if she could be talking about Farah, or indeed Amina, women who, in a very different context, also defied expectation. Could this be another reason for Freudenberger's interest in foreign cultures – that it allows her to create characters operating within the sort of moral restrictions that existed in the west in previous eras? "Yes," she says. "In order to have a marriage plot you need society to have rules and conventions. It's hard to write something that takes place in contemporary America where you feel the stakes are really high. You are never really shocked by the decisions that your friends make. You've heard all the stories before and no one is really ostracised."

Freudenberger's fiction itself, it strikes me, is similar in many ways to the marriage she depicts in The Newlyweds: an intriguing blend of old and new, the conventional and unorthodox. She applies a rather old-fashioned literary and moral sensibility to contemporary life, and in the process creates work at once familiar and surprising. And what of her own views on marriage? Does she think "arranged" unions have some advantages over love matches?

"Whether or not a marriage works," she says, "has less to do with how the couple met than with how much work they're willing to put into it while they're together. In that sense, Amina and George's marriage has as good a chance of working out as that of anyone else."