All four met at a party at the annual Twins Days Festival in Twinsburg, Ohio in 2017.
Jeremy and Josh went on to propose at the same time and, naturally, with matching diamond rings.
They all returned to the festival the following year and tied the knot in matching outfits. Brittany married Josh, and Briana married Jeremy, and now they all live together in a house in Virginia.
The first pair had their son Jett Salyers in late 2020, while the other couple welcomed Jax Salyers five months later.
In a recent video posted by the families on social media Jett can be seen pointing at his father Josh, and uncle Jeremy, and saying "Two dadas!"
Asked how many mothers he has, he squeals "Two!"
The couples say they are raising the children as if they are all parents to both of them.
Brittany said: "Technically, Josh and I are the parents of baby Jett. I gave birth to Jett.
"But really Jett has four biological parents because Briana and I share DNA. Josh and Jeremy share DNA. So we are raising baby Jett as though he has four parents."
She added: "It seemed like a perfect next step because it really does take a pair of twins to understand the special relationship of twins."
Such is the symmetry of their relationships that the older twins even married each other. Briana is five minutes older than Brittany, and Jeremy is five minutes older than Josh.
Jeremy told the Washington Post it made sense for identical twins to marry other identical twins, which is known as a "quaternary marriage".
He said: "Both of us always knew that we wanted to marry twins. We'd decided that if we couldn't find twins to marry, then we just wouldn't get married."
Briana said: "It's a pretty unique situation, but to us it seems really natural. Ever since we were little girls, we'd always dreamed of marrying identical twin brothers."
The brothers proposed on February 2, 2018, deliberately choosing the date 02-02.
"It couldn't have been more romantic," said Briana. "You can't do better than 02-02 to represent a double proposal and a double marriage."
The two brothers now run a wedding venue on a lake in Virginia, and their wives are both lawyers who work for the same law firm.
Josh said: "It's important that we all get along, and we do. That's what keeps everything afloat."
The terms "quaternary marriage" and "quaternary twins" were coined in the 1970s by psychiatrist Robert Ravioli. He said such relationships brought emotional benefits for the couples.
Ravioli coined the term "quaternary marriage" in an article for the New York Times in 1972. He looked at research into 50 such marriages and found that the divorce rate was far below the average. When there was a divorce, both couples did so.
He wrote: "As I pursued my own studies of these extraordinary and complex marriages, I became increasingly impressed with their success in withstanding the two forces - economic and child‐rearing - that are tearing so many other families apart today."
The benefits included being better off financially by sharing a house. He added that there was no evidence of "mate swapping".
He said: "Do the husband‐wife pairs ever criss-cross sexually? My studies to date indicate that they do not."
It is not known how many quaternary couples there are in the world, but Briana said: "There's only 300 quaternary marriages known in the history of the world."
The two sisters have featured on a US TV programme called 'Extreme Sisters'.
They describe their marriages as a "magical existence" and say their "dream has come true".
For them, there is only one thing left, and that is more children.
Both couples are hoping to have twins next time.
