Thrashing out the details of their new marriage contract with online relationship coach Suzie Johnson, the wealthy couple who have been wed for 12 years leave their hourlong Skype session feeling satisfied.

The husband agrees they can have a fifth child — while the wife consents to an infidelity clause allowing him to cheat with other women on a strictly annual basis.

“They agreed to a weekend amnesty, where the guy can do what he wants for just one weekend a year,” recalls Johnson, who runs the Dallas, Texas-based goasksuzie.com. “In return, she gets the bigger family she craved.”

According to Johnson, such arrangements are increasingly common in her practice as a growing number of women agree to “widen their monogamy boundaries” and embrace a marriage of convenience, where it’s just the husband who strays rather than an open marriage where both sides cheat.

It’s a fascinating trend that came into the spotlight this week with the death of 75-year-old Linda Jones, superstar Welsh singer Tom Jones’ long-suffering wife, who put up with his legendary philandering for 59 years.

Well-known public figures in similar situations include, most famously, presidential candidate Hillary Clinton, as well as Masha Lopatova, spouse of former NBA player Andrei Kirilenko. The mother of four admitted in 2006 that she sets the 6-foot-9 Russian-born athlete “free” once a year so he can sow his wild oats.

Citing 2013 study research that shows more than 50 percent of marriages survive infidelity, Johnson explains: “Fifteen years ago, having an affair would be a deal-breaker, but people now realize that it’s not the end of the world. It’s tough in the initial stages, but many see it as an opportunity to make a fresh deal.

“The more invested you are in your marriage — whether because of love, lifestyle, finances, children or a combination of those things — the more likely you are to make compromises [such as allowing the husband to cheat] to anchor the commitment.”

Rather than taking the open-marriage route popular in Europe, in America, it’s usually a case of “don’t ask, don’t tell,” where the wife turns a blind eye to the man’s peccadilloes. Another option, as psychotherapist Joe Kort asserts, is the “eyes wide open” approach that involves a written contract full of rules.

“For example, the woman might agree that the man can attend BDSM play parties once a month or have oral sex — not penetrative sex — once a week, so long as he has blood tests every three months,” says Kort, of Detroit, who often advises clients in mixed-orientation marriage — with one straight spouse and one who’s gay.

Pittsburgh-based former HR executive Sophie, 61, who asked that her last name be withheld to protect her privacy, fits into that category. When her physician husband admitted to a same-sex fling during a business trip in 2006, she remained by his side. “He said it was a mistake, and he was confused by his sexuality,” Sophie tells The Post.

Then, two years ago, he dropped the bombshell that he now considered himself gay and was actively seeking other partners.

“When it first happened, I thought I was going to lose my mind,” admits Sophie, who last had sex with her husband in the fall. “But, with help from Joe [Kort], we’ve figured out our arrangement.”

The couple, who have no kids, recently bought an apartment in New York City to serve as the husband’s love nest. Other times, Sophie visits the condo when she wants to catch a Broadway show.

So what made her decide to stand by her man? “We’re still very much in love and we have a rich history together,” says Sophie, who has been married for 33 years. “My parents are elderly, and I don’t see any point in telling them and hurting them by getting divorced.”

Other factors include the duo’s comfortable lifestyle in the Pennsylvania countryside and their devotion to their two dogs. But it’s been a difficult road, especially after Sophie confided in her sister and a rigidly Christian friend.

“They are very judgmental and think there is only room for two people in a marriage,” she says. “But, as Joe counsels me, you get to write your own story, and nobody can tell us how to live our lives.”