There are a lot of great big-band recordings from the stereo era.
Terry Gibbs' Dream Band. Seven CDs worth of live recordings from 1958/59 recorded by the great Wally Heider.
Ellington at Newport 1956. "Accidental" stereo. Originally issued in mono, and comprising mostly studio retakes with fake audience noises mixed in due to issues with Columbia's on-stage mic placement, a few years ago a full tape of from Voice of America using a different mic was discovered. The Columbia and VOA tapes were synced. The result is imperfect but very vivid, placing you right on stage with the band. One of the most thrilling performances in jazz history, this led to a meteoric revival of Ellington's career that continued to his death 20 years later.
Duke Ellington, The Great Paris Concert. Some oddities in the mix but basically a great recording, showing the Ellington band at the height of it's post-Newport powers. Includes a wonderful version of Suite Thursday.
Duke Ellington and Count Basie, First Time! Studio recording from 1961. Some distortion on the original tapes but great playing from both bands. Be sure you get the 1999 reissue with bonus tracks.
Benny Goodman, Benny in Brussels. Not stereo but a good recording and great playing from everyone.
Woody Herman, Harry James, Les Brown and other classic band leaders made excellent recordings throught the 50's and 60's.