the red carpet together, Davidson in black Vans and a Prada suit and sunglasses, Kardashian in a glittering silver Balenciaga Couture dress with Lorraine Schwartz jewelry. She wore her black hair down in waves.

They had an affectionate moment on the carpet:

The two's D.C. date comes one week after they attended the 23rd Annual Mark Twain Prize for American Humor ceremony in the city.

Earlier this month, a source spoke to Peopleabout Kardashian and Davidson's romantic relationship. Her family “enjoy[s] having him around,” the source said. “He is great for Kim. He is getting to know her kids and everyone seems to be getting along. Pete hasn’t had any expectations. He gets that he is coming into a complex family situation. He doesn’t want to complicate things.”

“It was difficult for Kim to see herself dating [after her divorce from Kanye West],” the source continued. “Dating Pete has been amazing for her though. She feels very lucky.”

Kardashian spoke about Davidson herself during her recent interview on ABC News. “I am a relationship kind of girl, for sure, and I wouldn’t be with someone if I didn’t plan on spending a lot of my time with them,” she said. “Obviously, I want to take my time, but I’m very happy and very content. And, it’s such a good feeling to be at peace.”