"It's an easy relationship since they have known each other for so long," a source tells PEOPLE

Kourtney Kardashian and Travis Barker are enjoying some quality time together. 

The Keeping Up with the Kardashians star and Blink-182 musician were spotted having dinner at Matsuhisa in Los Angeles on Tuesday. Both donned black leather jackets for the occasion and held hands throughout the meal.

"They sat across from each other, enjoyed the food and chatted," a source tells PEOPLE of the new couple's date night. "They seemed to have a great time. They flirted and were smiling. They even held hands across the table. Kourtney looked very happy."

Kourtney Kardashian and Travis Barker

Another insider adds that the stars put their kids first, but try to squeeze in some one-on-one time as well.

"They spend most of their time together with the kids, but they have tried to sneak away for dates without the kids, too," the insider says. "It's an easy relationship since they have known each other for so long. Kourtney knows what Travis likes and they have a lot in common."

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 2004-2008.

Kardashian, 41, is also a mom of three and shares sons Mason, 11, and Reign, 6, as well as daughter Penelope, 8, with ex Scott Disick. Kardashian and Disick, 37, ended their nine-year relationship in 2015.

"They both prioritize their kids so there is no conflict there," the insider says of Kardashian and Barker. "Kourtney is having a great time with Travis."

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

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PEOPLE confirmed Kardashian and Barker's relationship last month after the couple spent a weekend together at Kris Jenner's Palm Springs home.

"They've been dating for about a month or two," a source told PEOPLE at the time. "They've been friends for a long time but it's turned romantic."

While their relationship is still in the early stages, another source said Barker has already gotten the stamp of approval from Kardashian's famous family.

"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," said the source. "Her family and friends all really like him. Their kids all get along too, which is sweet."