Han Solo and Leia Organa had their ups and downs during the original Star Wars trilogy, but once the second Death Star was destroyed and the Empire was dealt its heaviest blow ever, those two crazy kids finally embraced their romantic feelings for one another. Oh sure, there was that time on Cloud City, but having one of them frozen in carbonite really kills the mood. Anyway, they were ready to start a life together, which was why it was sad to learn in The Force Awakens that they had separated years earlier. Their son Ben turning to the dark side and becoming Kylo Ren was the ultimate reason for the separation, but an excerpt from an upcoming Star Wars book indicates their relationship had issues that couldn't have been resolved.
Star Wars Aftermath: Empire's End is hitting bookshelves later this month, and will conclude the Aftermath trilogy written by Chuck Wendig, which explores that galaxy far, far away in the immediate years after Return of the Jedi. An earlier excerpt from the book shed some light on what happened to Lando Calrissian, but this excerpt directly from StarWars.com delves into an especially fun time for Han and Leia: the latter being pregnant with Ben. Han has been helping the best he can, which includes getting her jogan fruit, but Leia can see that this process is difficult for him. One part notes:
It's been hard for Han. He won't say it out loud, but she can see it on his face. Her husband needs something to do. He's bored. Chewbacca's back home, looking for his family. Luke's searching the galaxy for old Jedi teachings. Han Solo's got nothing to smuggle, nowhere to gamble, no foolish Rebellion to fight for.
Also putting a strain on their marriage is how Leia is eager to "unofficially" help liberate worlds still controlled by the Empire or criminal organizations, and persuade them to join the New Republic. Han isn't fond of doing this, not only because he's concerned for his wife's safety, but also because he considers the last time they pulled off a mission like that, on Kashyyyk, to be a "fluke." Overall, though, it's clear that despite their love for one another, Han and Leia are still very different people. Leia is still dedicated to her governmental duties and improving the galaxy, while Han just wants to go adventuring, be it for fun or to make some money as a smuggler.
Even if their son hadn't joined the Knights of Ren, it seems likely that Han and Leia would have eventually separated. It probably wouldn't have been nearly as tragic or devastating as what went down in the years before The Force Awakens, but something would have happened that created a wedge too deep to mend. The best hope in that instance is that they could at least have maintained somewhat of a connection with one another, rather than go a long time without communication. It's also worth mentioning that when Han enters the Empire's End scene, he calls his son a "little bandit," while Leia prefers to think of him as a "little angel." Given how the father/son relationship ultimately played out, "bandit" was the more apt term.
While Han Solo met his demise at Kylo Ren's hands in Star Wars: The Force Awakens, you can see his younger self in action when the Han Solo movie is released on May 25, 2018. As for Leia, she'll appear in Star Wars: The Last Jedi on December 15, but there's no word yet on how the character will be handled in 2019's Episode IX following Carrie Fisher's passing.