@coltrane1: Give a listen to "Rag Mama Rag" by The Band. On this song pianist Richard Manuel takes Levon Helm’s place on the drumset, organist Garth Hudson moving over to piano. Hudson is very much a fan and student of Jazz (he loves the playing of Bill Evans. Who doesn’t? ;-), and on this song he displays his abilities in the "stride" style of piano playing, popularized by the likes of Fats Waller. And that's just one song on this "perfect" album.
When The Hawks (The Band’s name up until 1968) were playing the clubs in Toronto in the early-to-mid 1960’s, they were taking in shows of USA artists who were passing through town, artists such as Cannonball Adderley and Ray Charles. When The Band headlined a show at The Hollywood Bowl in 1970, they were given carte blanche to pick their opening act. They chose Miles Davis. I can’t think of another Rock band who would do that. Miles’ drummer Jack DeJohnette and Levon Helm became very close friends, and when DeJohnette himself headlined the 2017 Playboy Jazz Festival at The Hollywood Bowl, he included The Band’s "Up On Cripple Creek" in his set.
Also listen to The Band’s live album Rock Of Ages, recorded at The Academy Of Music in NYC. For those shows they hired Allen Toussaint to write horn charts for their songs, and to hire the players to perform them. The horns provide a real New Orleans (Toussaint’s hometown) feel, very cool.
Another Rock ’n’ Roll band with a heavy Jazz influence is NRBQ. Pianist Terry Adams is particularly fond of Thelonious Monk and Sun Ra. Terry himself plays with wild abandon live, pounding out wild runs on his electric piano and clavichord. If NRBQ ever comes to your area, don’t miss their show! One of the greatest live bands I’ve ever seen and heard. Most fun too.