We have investigated the shear flow behavior of a classical viscoelastic equimolar wormlike micellar system made of cetyltrimethylammonium bromide and potassium bromide in the semidilute regime using mechanical and optical measurements. The experimental flow curve of this surfactant solution exhibits, above a critical shear rate, a well-defined stress plateau, characteristic of a flow of the shear-banding type. We first focus on the rheological and rheo-optical transient response of the sample after the sudden start-up of flow. The time-dependent stress profiles are strongly similar to those observed on various other systems with the occurrence of an overshoot at short times followed by a stretched exponential relaxation toward the steady state on a long time scale. This behavior is then correlated to the temporal evolution of the birefringence intensity and the extinction angle; the latter exhibits an undershoot just after the inception of the flow. Using direct visualizations of the sheared sample and spatially resolved flow birefringence accross the gap of the Couette cell, we have been able to highlight a peculiar banding structure made up of three distinct regions: two layers of homogeneous but strongly differing orientations located against the walls, separated by a mixed layer, the width of which can reach half of the gap as a function of the effective applied shear rate. The induced structures contained in the band adjacent to the inner moving cylinder are found to be almost fully aligned along the flow direction. The relative proportions of each region are derived from the orientation profiles and compared to the predictions of the lever rule. The results suggest that orientation bands and shear bands are not linked in an obvious way, and the observed band structure can finally be interpreted as the coexistence either of three distinct "phases" or of only two homogeneous phases separated by an interface which can be broad, or thin and fluctuating.