Jazz blues

Jazz blues (or blues jazz) can be any musical style that combines jazz and blues. However, since jazz is considered to have its roots in the blues, it almost always contains blues elements such as blue notes, blues-like phrasing of melodies, and blues riffs. Therefore the terms are generally used to refer to bands or musicians that have a distinctly blues style or feel, while also making use of other harmonic or melodic devices commonly associated with jazz.

The term jazz blues is also commonly used by jazz musicians to refer specifically to a tune that follows the standard Twelve-bar blues chord progression, while altering the chord progression and improvisation to fit a jazz style. Such tunes are extremely common in the jazz repertoire.

Source : http://en.wikipedia.org/wiki/Jazz_blues