Happy Marriage Charade

Alice and Bob met. They fell in love. They got married. And everyone around them thought they were perfect together.

But the course of true love—or even raging hormones—never did run smooth. And eventually things begin to get a little rocky.

But Bob's family will cut him off if he gets a divorce! Alice won't get her inheritance if she doesn't have a child born in wedlock! The family will be subjected to the scrutiny of the media and embarrassment from same if it gets out that the perfect couple—isn't. Or there's some political reason that would make things complicated and unpleasant if they divorced. Or divorce is against their religion.

So they leave the marriage intact on paper and work out an agreement to hold up appearances, while secretly getting on with their separate lives.

If Alice and Bob aren't really in love because Bob loves Chuck, then Alice is The Beard and the marriage is still a charade.

Sometimes the couple hates each other but pretends they're happy to the outside world.

Compare Sexless Marriage and Citizenship Marriage.

Fan Works

 * In the Glee fanfic When The Lights Go Out, Will You Take Me With you?, Blaine's parents have this, which works out well for them, since they both have jobs that include a lot of traveling. Basically, they avoid being in the same place at the same time, including the family's house in Ohio. Because of that, it takes them four months to realize that their 17-year-old son has run away and is now living with his boyfriend in New York.
 * Starfall of Summer Days and Evening Flames has a complicated relationship with his wife. Since she's a pegasus who lost her wings by a griffin attack, he's held a view of her as "damaged goods" and is rather cold. He's actually the last person to realize this among his circle of coworkers.
 * In the Tintin fanfic An Evening at the Airport the author suggests that the Waggs put on one of these.

Film

 * In the film version of The Count of Monte Cristo (not sure about the book), Mercedes and Fernand are in one of these when Edmund returns from the Chateau d'If. The facade has been thoroughly broken by the end.
 * Dave had the (real) President and First Lady unable to stay in the same room or look at each other unless the press was watching, at which time they both play the loving couple. He only stays married for his career image (and has plenty of affairs) and she only stays so she can do important work with charities.
 * Who's Afraid of Virginia Woolf?: Jury's still out on which of the two couples has the shakiest marriage.
 * Though George and Martha have almost the opposite. They fight bitterly in front of everyone and yet would never genuinely leave the other, preferring to spend their life to making the other miserable. Nick and Honey however are this trope.

Literature

 * Oscar and Judie Valentine of the Lucy Valentine series are still married on paper. In fact, they're still good friends and occasional lovers, though they maintain separate residences, and Oscar tends to philander. But Oscar's family business is matchmaking and it would be a blow to the business—and their wallets—if the King of Love were revealed to be having a failure to achieve marital bliss. So they hang out together and do social events together to keep up appearances.
 * Everett and Ivy Noble of Heroine Addiction are also still happily married on paper. Why? They're both superheroes, and the toast of the town to boot. But even juicier?  So they go through the motions in public of being happily married, including a date night.
 * Agatha Christie uses this trope liberally:
 * In "The Mysterious Affair at Styles", John and Mary Cavendish. Mary was not in love in John when they got married and he eventually forms an affair with another woman. Subverted in the end because she finally falls in love with him and he finds out, thus leading to an actual happy marriage.
 * In "A Caribbean Mystery", roughly the same storyline is played with Edward and Evelyn Hillingdon.
 * Maryse and Robert Lightwood in The Mortal Instruments only pretend to be Happily Married, when in reality their marriage has nearly fallen apart at least thrice: once when the Circle disbanded and Robert blamed their wrecked lives on Maryse, twice when, and thrice when  . The general distrust between her parents lead to Isabelle's "all-men-are-untrustable" attitude.

Live Action TV

 * John And Mary on Father Ted, married shopkeepers who are always plotting to murder each other, but who go into over-the-top perfect couple mode whenever anyone else is around.
 * Lindsey and Melanie do this in Queer as Folk after they separate when Lindsey cheated on Melanie with a man. Needless to say, they got found out.

Real Life

 * In real life, many unhappy couples remain married and pretend not to hate each other for the sake of their kids.

Western Animation
"Look, I'm sorry. A loveless marriage is one thing, we're not hurting anybody. But bringing a child into a loveless family is something I just can't do."
 * The Simpsons: Selma almost got into one of these with Troy McClure, so he could salvage his career. But when he wanted to have a baby, that queered the deal for her.