updated 04/01/2014 AT 4:00 PM ET
•originally published 04/02/2014 AT 8:00 AM ET
In this week’s cover story, several friends tell PEOPLE that the pair, who were married for 10 years, at times had an “open” relationship.
“They were physically separated and emotionally,” says a Paltrow insider.
Adds a close friend of the 41-year-old actress: “They have been on and off for many years. The marriage was falling apart.”
Personality conflicts and distance proved challenging for the couple, who are parents to daughter Apple, 9½, and son Moses, who turns 8 next week.
The Coldplay rocker, 37, “is the kind of person who is always in a T-shirt,” says another friend. “She’s much more glam.”
With two busy careers to sustain, “they seemed to have a pretty mature handle on that crazy rotation of being superstars and parents,” says a source who knows them both. “But that balance, given the time they had to spend apart, clearly couldn’t sustain itself.”
For much more on this story, including a closer look at the splitting stars’s fortune and exclusive details on their Bahamas breakup moon, pick up this week’s issue of PEOPLE.