"It just comes natural, it's like a maturity thing," Travis Barker said of his current relationship and dating a fellow parent

Appearing on Drew Barrymore's CBS talk show Thursday, the Blink-182 drummer, 45, opened up about his relationship with the Keeping Up with the Kardashian reality star.

Though Barker did not mention Kardashian by name as Barrymore, 46, simply called her his "lovely lady," they spoke about a love note the Poosh founder, 41, recently wrote to him.

"My love note would be like, 'Can we get to bed early and watch a movie?' " Barrymore joked about Kardashian's "hot" love note to Barker, which read: "To lots of fun adventures. May we destroy each other completely. Love, Kourtney."

"I would prefer the opposite. I would prefer to, kind of, go in the blaze of glory and ball of flames," said the musician, who was a longtime friend of his girlfriend's before things turned romantic. The couple made their relationship Instagram official in February after a source told PEOPLE in January that they were dating.

Kourtney Kardashian note to Travis Barker
Credit: Travis Barker/Instagram

And when Barrymore asked the Barker Wellness founder if he thinks "it's better" to date someone with kids versus someone who is not yet a parent.

"I've done both up until now. I dated girls who didn't have kids and I find it hard because they would have trouble understanding like, 'Why don't you want to go to dinner every night with me?' or 'Why don't you want to see me every night?' And now I'm spending time with a woman who's a great mom, who's a great friend and you don't have to worry about any of those things," Barker said.

"It just comes natural, it's like a maturity thing. And I also really like missing someone and cherishing the time that I spend with them instead of every day being with them, especially in the beginning of the relationship. I think missing someone is so important," the father of three added.

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Barker 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.

Meanwhile, Kardashian 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. (Disick is now dating model Amelia Hamlin.)

Elsewhere in his Drew Barrymore Show interview, Barker spoke about parenting his kids, who have been touring with him since age 2.

"I can't protect them from everything, I can't shelter them from everything," he said. "All I can do is, kind of, show what doors that I walked through and what worked for me and what didn't work for me. And protect them and guide them as much as I can."

A source recently told PEOPLE that Barker and Kardashian see their romance as "something positive," adding that "Kourtney is very happy with Travis. She feels very fortunate. She loves spending time with Travis."