Jughead only developed an interest in the Blossom family after he began writing about the mysterious death of Cheryl's brother Jason Blossom. Even then, he never approached Cheryl about the subject directly.
Jughead was one of several students to attend Jason Blossom's Memorial, though his motivation for doing so was to investigate the Blossom home with Betty Cooper to search for clues to Jason's death. He was as stunned as anyone when Cheryl arrived in a white dress.
Jughead and Betty later confronted Cheryl about Betty's sister Polly Cooper, who was staying at the Blossom house and wanting to hear from her. Jughead and Cheryl traded barbs during the confrontation, with Jughead essentially accusing the Blossom family of holding Polly hostage and Cheryl calling Jughead a "hobo"..
Jughead was angered when Cheryl and Chuck Clayton crashed his birthday party with dozens of other kids in tow, intentionally turning what Jughead had hoped would be a small, intimate affair into what Jughead described as a "Seth Rogen movie". It should be noted, however that Cheryl and Chuck were motivated by revenge towards Veronica Lodge and Betty, respectively, rather than any direct malice towards Jughead. Jughead attempted to leave the party, but was blocked by Cheryl and Chuck. Their attempt at a "Secrets and Sins" game, revealing embarrassing secrets Betty, led to a brief brawl between Jughead and Chuck, before Jughead's father FP Jones ejected Chuck from the house and told Cheryl the other kids to leave.
After FP confessed to the murder of Jason, a shaken and humbled Jughead approached Cheryl in the school cafeteria and apologized for his father's supposed actions. Cheryl responded, however by slapping and hitting him repeatedly before she was pulled off him by Archie Andrews.
Days later, after it was determined that Jason was in fact killed by his and Cheryl's father Cliff Blossom (who took his own life shortly after being exposed), Cheryl approached Jughead in the cafeteria and apologized for pummeling him. Cheryl gave him her iconic spider broach as recompense.
After Veronica received a text from Cheryl apparently declaring her intent to take her own life, Jughead hurried with Veronica, Archie, and Betty hurried to Sweetwater River to stop her. After she fell through the ice, Jughead noticed that she was being pulled by the current and instructed the others to spread out in order to find her. Cheryl was saved by Archie moments later.