Industrial fluid flow through pipes and ducts are never smooth and will experience some degree of surface roughness. Turbulent plane-Couette flow (pCf) between two walls in relative motion is one of the classical problems in fluid mechanics. Barring one experimental study, no information on turbulent pCf with surface roughness exists in the literature. This is surprising considering the practical relevance and the canonical nature of the problem. In this direct numerical simulation (DNS) study, a fully-developed turbulent pCf, where the bottom-wall is roughened and the top smooth wall moves with a constant velocity Uw, is reported. For roughening, roughness elements in the form of square ribs of height r = 0.2h (where h is channel half height) are mounted only on the bottom wall with streamwise pitch separations of 5r and 10r. Upon roughening a wall, roughness would generate vortical structures near the vicinity of the roughness elements and enhance turbulence locally. We report that in the current problem, turbulence kinetic energy (TKE) is enhanced near both the rough- and the smooth-walls. The major factor aiding this process is the blockage effect offered by the rib-roughness, which enhances the skin-friction on both the walls, and therefore the average friction Reynolds number is increased by 25% and 33% in the cases with pitches 5r and 10r, respectively. The time series of spanwise vorticity fluctuation in the case of s = 10r shows the presence of coherent Kelvin-Helmholtz-like structures behind the ribs. Phase analysis using Hilbert transform reveals that the flow within the cavity for the s = 5r case is in-phase, while a phase shift is observed for the s = 10r case. Anisotropy tensors and anisotropic invariant maps are used to explore turbulence anisotropy at both large- and small-scales of motion. It is observed that anisotropy is reduced in both the cases near the vicinity of roughness.