Alice and Bob met. They fell in love. They got married. Everyone around them thought they were perfect together.
However, the course of true love — or raging hormones — never did run smooth. Eventually things get a little rocky but the couple can't break up.
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. There could be 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 or Alice loves Danielle, then either Alice or Bob is The Beard and the marriage is still a charade.
Sometimes the couple hates each other but is obsessed with keeping up appearances.
Compare Sexless Marriage and Citizenship Marriage. For the Dom Com genre, see Awful Wedded Life.
Soichiro and Sumi's marriage at first. Soichirou needs to get married to inherit his fortune, Sumi needs money to support her very poor family, and they reach an angreement over marrying without love.
Nozomu also thinks this way towards his own marriage with Miu. He also nees to marry to get his position secured, while Miu is an Impoverished Patrician. At the very end, they seem to have gotten better.
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.
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.
Nick and Honey from Who's Afraid of Virginia Woolf?, unlike George and Martha who fight bitterly in front of everyone, and yet they are too emotionally dependent on each other to seriously consider divorcing. They seem to be happily married, yet Nick only married Honey for her father's money (the fact that she was pregnant was a convenient excuse) and Honey is implied to have aborted her baby after marrying Nick, and when Honey drinks herself sick, Nick goes to bed with Martha.
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? Everett actually left Ivy for a guy named Morris Kemp — who is a supervillain, and one of the family's arch enemies. So they go through the motions in public of being happily married, including a date night.
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.
Inverted in Evil Under the Sun. Patrick and Christine are a happily married couple, but pretend their marriage is on the rocks in order to cover up their murder of Arlena.
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 Robert was caught cheating (but Maryse told nobody save her daughter), and thrice when their youngest son dies. The general distrust between her parents lead to Isabelle's "all-men-are-untrustable" attitude.
In Daphne Du Maurier's Rebecca, Maxim and Rebecca.
In Summers at Castle Auburn, Bryan and Elisandra know how to put on the performance of future king and queen and look good together (Corie notes that they are fantastic dance partners for example), but they don't love each other, or even like each other. They don't even have anything to say about each other. But politics demand they marry anyway.
William and Nora Walker on Brothers and Sisters. William works hard to preserve a personal and professional image as a conservative, traditionalist, husband, father and businessman. In reality he is supporting a mistress on the side in a decades-long affair that is virtually a second marriage, while at the same time having short-term affairs with other women as well. His wife learns of the affair but goes into willful denial when he promises to end it. When he dies the truth comes out, and it is devastating to his whole family. Especially his daughter Kitty, a conservative pundit who has held her parents' marriage up as a role model all her life, and the youngest son Justin, who had gone to war to try to win his father's respect, only to learn how sleazy his father really was.
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.
Stevie's parents apparently did this in Malcolm in the Middle, to protect Stevie while he was still very much unwell. When she felt Stevie was now old and strong enough to handle it, Stevie's mom left her husband and Stevie.
This is the situation behind Los Exitosos Pells. The husband is gay, the wife is just on there for the career bust, and both are planing to elope with their real love interest at the first chance, but both are forced to being together because their network contracts, and have to keep the happy charade for ratings sake. The hero, who is forced by the same network to secretly impersonate the husband after an accident, is quite on shock when he discovers all of the above.
In Demo Reel, Donnie desperately tries to convince other (and even himself) that he is happily married with his very cold and distant wife, and as long as they are not in the same room he is almost convincing. But when you have a prenup that explicitly forbids you and your partner to appear together in family gatherings, that's quite the facade to maintain.