In “Harley Quinn” season 3, both Commissioner Gordon and the semi-reformed (emphasis on “semi”) Joker run for mayor. The race comes to a head in episode 6, “Joker: The Killing Vote.” Gordon recruits Two-Face to be his campaign manager; after all, Harvey Dent does have experience winning public office in Gotham City.
Two-Face’s strategy involves kidnapping the Joker’s stepson Benicio. When Gordon objects, Two-Face says they’re “In Too Deep” and starts unknowingly quoting the lyrics from said Sum 41 song: “And I’m trying to keep up above in my head, instead of going under, instead of going under!” That’s when he catches himself, explaining he heard the song earlier on the radio while driving.
According to Halpern, the joke came from the episode’s writer Conner Shin. Before he approved it, he asked Shin what the context was:
“When I read that joke, I was like, ‘Why would Two-Face be listening to this?’ And then Conner was like, ‘Well, he’s about 40. And that’s when he was probably listening to — whatever you’re listening to when you’re 21, 22 just becomes the soundtrack of your life.’ And I was like, ‘I’m sold. Put that joke in there.'”
“In Too Deep” was released in 2001. If Two-Face is indeed 40 in the episode, then he would’ve been born in 1982, just the right age for the song to be a staple of his transition from adolescence to adulthood.
“Harley Quinn” is filled with these sorts of pop culture jokes. They make the characters feel a bit more ridiculous, yet conversely, also more human. In this rendition of Gotham City, supervillains listen to rock music too. At least Two-Face has good taste.