The bittersweet episode, which was taped a week before 41-year-old Bennington committed suicide, opens with Jeong getting into the front seat of the auto and asking if he can join the rock band.
Before the episode was released, Bennington's family was consulted to make sure they were okay with the video.
The group sings Outkast's "Hey Ya", Linkin Park's "Numb", "In The End" and "Talking to Myself", and Red Hot Chili Peppers" "Under the Bridge'.
A somber message appears before the video starts: "With the Blessing of Chester's family and bandmates, we share this episode and dedicate it to the memory of Chester".
Later in the clip, the group moves from a Cadillac SUV to a party bus, where they sing Lynyrd Skynyrd's "Sweet Home Alabama" and "I Don't Wanna Miss a Thing" by Aerosmith.
As well as singing along, Bennington also took some time tutoring Jeong in the art of "scringing" - a portmanteau of screaming and singing.
"One of my kids loves sports", the singer said.
"In memory of Chester Bennington: March 20, 2017 - July 20, 2017". The episode was filmed a week before Bennington's death. "Where does the music come from?' I want them to find whatever it is". Because Lilly is really curious, asking 'Daddy how do you write songs?
Bennington is survived by wife Talinda and six children: Jaime, Isiah, Draven Sebastian, Tyler Lee, and twin daughters Lily, and Lila.
Linkin Park will hold a benefit concert in honor of Bennington October 27 in Los Angeles.
The episode was shared on Linkin Park's Facebook page on Thursday, and a special dedication to the late musician ran at the beginning.