And they are making good on that promise.
In an interview Thursday about the upcoming PBR World Finals, Murray told PEOPLE, "It's going good with me and [Kase]'s mom. She and I always think of Kase first. It's been great, it truly has. I feel really fortunate and lucky for that."
Added Murray: "I do feel like we are friends. That's really important to me on a lot of levels. We're all in a really good spot and we're all getting all our needs met."
On Tuesday and again on Thursday, Jewel (who said last month she's "doing good" post-split), posted pictures of her estranged husband and their son on her Instagram page.
"My two favorite cowboys," she wrote alongside Tuesday's photo of the boys, who wore matching smiles and cowboy hats.
My two favorite cowboys
Two days later, she shared another photo of Murray and Kase – still in their hats – captioned, "@typbr and Kase all Cowboy'd up."
@typbr and Kase all Cowboy'd up... #Texas
The singer and the former world champion cowboy and Professional Bull Riders star were together for a decade before quietly marrying in the Bahamas in 2008. Jewel announced their split on her blog in July.
"For some time we have been engaged in private and difficult, but thoughtful and tender undoing of ourselves," she wrote. "Ty and I have always tried to live the most authentic life possible, and we wanted our separation as husband and wife to be nothing less loving than the way we came together."
"Due to the spirit in which we have gone about this separation, we trust we can remain dear friends who hold each other in high esteem, which is so important to us as parents – we wish only what is best for our son."