Inside Katy Perry and John Mayer's Rekindled Romance: 'They Are in Love'
01/15/2015 AT 07:15 AM EST
Sharing a romantic double date with pals Allison Williams and her fiancé Ricky Van Veen at the Chateau Marmont on Saturday, the singers – who have split three times in the last two years – looked every bit the loved-up couple, holding hands and sharing kisses at the table.
"They are in love," a Perry insider tells PEOPLE of the pair, who have been having sleepovers and low-key dinners with friends. "They missed each other."
Though the two clashed over Perry's hot career in their last go-around, "they seem very happy about being back together again," says another source, who notes the duo have always had great chemistry together.
For now, Perry, 30, and Mayer, 37, are enjoying spending time together, but the insider says the two still have to figure out how to balance their personal and professional lives.
"They have to make time for each other and figure out how they can be together in a smooth relationship," the source says.
Reporting by STEVE HELLING and LINDA MARX
For more on Perry and Mayer's romance, pick up the latest issue of PEOPLE Magazine, on stands Friday