“Jen has made a few visits to his Malibu house,” says a source. “Chris seems very respectful of Gwyneth and feels more comfortable spending time with Jen away from his family.”
Lawrence, 24, and Martin, 37, also stepped out for a romantic date night at Beverly Hills eatery La Dolce Vita on Sept. 8, where an onlooker says the new couple “were super cute together and laughed a lot.”
On weekends, though, the singer has been all about his kids Apple, 10, and Moses, 8.
“Gwyneth and Chris take the kids for brunch or dinner together every weekend,” says the source. “He and Gwyneth still share responsibilities when it comes to their two kids.”
At the Hungry Cat restaurant in Santa Monica on Sept. 13, “they were very friendly to each other,” an onlooker tells PEOPLE about the pair, who did not wear their wedding rings. “They looked like a happy family.”