In this study, plane Poiseuille-Couette flow is simulated as a model for specified streamwise slip on one of the channel walls. The relative velocity between the two walls is set to be 1, 2, and 4 in viscous wall units. This is equivalent to the presence of a superhydrophobic surface at one of the channel walls that causes fluid to slip on the boundary. The results show that the streamwise slip forces turbulence in the near-wall region to tend towards a limiting one-component state. This leads to the suppression of small scale turbulence and laminarization close to the wall and then to drag reduction. The selective weakening of the streamwise vorticity close the wall and the observed decrease of turbulence kinetic energy production can then be considered as a consequence of this effect. Changes in the coherent structures, including a decrease of sweep events and increase of ejection events close to the wall where slip occurs, are also observed.