Before heading to L.A.'s Pantages Theatre for a show, the pop star and her former agent had a double dinner date with Trawick's mother and father at the Grafton on Sunset Hotel's Olive Kitchen + Bar.
They dined from about 5:30 p.m. to 7 p.m. on meatballs and margarita pizza, and an onlooker at the restaurant says Spears enjoyed the quality time with his folks.
"She seemed to fit in very well with his family," the source tells PEOPLE.com. "She seemed very comfortable. She was very warm to them."
As for Spears and Trawick, who have already fended off engagement rumors, they appeared to be a happy couple, keeping it romantic but low-key.
"Britney and Jason were really affectionate," the source says, "but at the same time very respectful."
Reporting by DAHVI SHIRA and JENNIFER GARCIA