Keri Russell & Matthew Rhys: Inside Their Love Story

Their spark was instantly undeniable.

The Americans stars Keri Russell and Matthew Rhys have starred opposite each other on the FX spy drama since 2013. And as their characters contended with the intricacies of a KGB-orchestrated marriage, Rhys and Russell embarked on a real-world love story off-screen.

Now, while the pair films the show's fourth season in New York City, they're anticipating the arrival of a baby together.

In 2013 after seven years of marriage, Russell split from Shane Deary, with whom she has a son River, 8, and a daughter Willa, 4. Russell's rep told PEOPLE at the time: "The separation is amicable, and their focus is on their children."

Nearly a month after news broke of the separation, rumors began to swirl about an off-screen relationship between Rhys, now 41, and Russell, now 39. Were the actors just so convincing at portraying the slow-burning intimacy between secret agents Elizabeth and Philip Jennings that it had been mistaken for genuine affection, or was there truth to the gossip? Evidence began to pile up in favor of the latter when the twosome was spotted walking around Russell's neighborhood in Brooklyn Heights a few days before Christmas 2013.

"They looked very much like a couple," a source told PEOPLE of the costars, who were seen shopping and looking at furniture. "They were laughing and walking closely together."

But just months later in February 2014, Rhys laughed off rumors about a brewing romance with his leading lady, telling PEOPLE he'd even had to deflect inquires from his mother.

"She calls up going, 'What's going on? I just read this about you,' " he told PEOPLE about his mom's habit of keeping up on reports about him. "I tell her, 'You have to take off your Google alerts.'"

Rhys said he found his mother's reaction to rumors that he and Russell were dating particularly amusing: "That is the best one I love. I've told her a million times that there are a million inaccuracies that she's read, [but she still] calls and goes, 'Is this true?' I tell her, 'No! When are you going to get it?'"

Later that month, Rhys did gush about the upbeat atmosphere on The Americans set.

"We do laugh a lot," he said. "Maybe a little too much, and it becomes a great struggle. It's not that you're trying to do the scene, it's that you're trying not to laugh during these intense scenes. There's a lot of practical jokes."

But the actor denied that his steamy scenes with Russell were a sign of any real-life passion. "We've all done a million of them in this crazy life we sign up for," he told PEOPLE about shooting racy sex scenes. "The first one is always the hardest, and then you realize there's a very perfunctory element to it where cameramen shout, 'Hand up more! Down with your elbow! Lift your leg up higher!' The clinical element of it kicks in, which sort of takes away from that embarrassment."

Meanwhile, Russell told The Los Angeles Times that acting opposite Rhys always felt "easy" and "safe." "What I enjoy is [Rhys] makes it so easy," she said. "You feel you're in safe hands, and it's enjoyable to work like that because you're sort of like, let him do all the hard stuff."

In March 2014, PEOPLE finally confirmed what fans had long suspected: Russell and Rhys were a couple.

The actors were seen cozying up at a performance of The Library at New York's Public Theater. Fellow theatergoers noticed Russell stroking her date's hair and the pair whispering to each other before leaving the show.

Then even bigger news broke in early January 2016: Rhys and Russell's next mission? Raising a child together.

"They're thrilled," a friend of the couple told PEOPLE about the pregnancy.

Just as it happened to their KGB characters on The Americans, what started as a relationship all for show evolved into authentic affection and, soon, a parenting partnership for Rhys and Russell.