i love big band music, it's my favorite type. it's just happy music that i can sing along with. but i have a pretty wide range of music i enjoy.
I have not really listened to 'big band' very much, but the way you describe the "band singing ....as part of the song" IS very enjoyable.
It makes me appreciate the song more, now, since I had mainly heard the music, and not really on how the band's singing complemented the song. Very unique.
i've never heard another group/band have the band singing as part of the song like that. one of glenn miller's songs comes close to it though, when they play/sing pennsylvania 6-5000.