Kourtney Kardashian and Travis Barker's "kids all get along too, which is sweet," a source tells PEOPLE

Kourtney Kardashian and Travis Barker's relationship has already received the stamp of approval from the reality star's famous family.

A source tells PEOPLE that the new couple has spent time with each other's families in the months since they started dating.

"He's liked her for a long time and she just got more open to the idea. He's a good guy and a really great dad," says the source. "Her family and friends all really like him. Their kids all get along too, which is sweet."

Kardashian, 41, and her ex Scott Disick co-parent their three kids: sons Mason, 11, and Reign, 6, as well as 8-year-old daughter Penelope. Kardashian and Disick, 37, ended their nine-year relationship in July 2015.

Meanwhile, Barker, 45, shares stepdaughter Atiana, 21, daughter Alabama, 15, and son Landon, 17, with his ex-wife, Shanna Moakler, whom he was married to from 2004-08.

"Travis is great guy. He is very nice to be around. Throughout their friendship, Travis has always had stronger feelings for Kourtney," a second source tells PEOPLE. "He has been pursuing her for a while."

Kourtney Kardashian, Travis Barker
Kourtney Kardashian (L); Travis Barker
| Credit: Charles Sykes/Bravo/NBCU Photo Bank/NBCUniversal via Getty Images; ABC via Getty Images

And while Kardashian's family is supportive of the relationship, the pair is "taking it slow."

"They are having fun. Kourtney's family likes Travis. He is a safe guy for Kourtney to date. They are taking it slow and it's not serious," says the second source.

A rep for Barker did not immediately respond to PEOPLE's request for comment.

Over the weekend, a source confirmed the relationship to PEOPLE, saying Barker and Kardashian have "been friends for a long time but it's turned romantic."

"They've been dating for about a month or two," said the source.

On Saturday, the Keeping Up with the Kardashians reality star and the Blink-182 drummer both shared poolside views from Palm Springs, California, during a quick getaway together.

Kourtney kardashian
Kourtney Kardashian
| Credit: Kourtney Kardashian/Instagram

Kardashian and Barker have known each other for years. In addition to living in the same Calabasas, California, community, Barker has previously made brief cameos on Keeping Up with the Kardashians.

Kardashian was previously romantically linked to Younes Bendjima and Luka Sabbat.