The shear-induced diffusivity of non-Brownian spheres in monodisperse suspensions undergoing viscous flow was calculated using simulations that account for particle roughness and friction as independent parameters. The diffusivity increases significantly as the friction coefficient is increased, and the effect is largest on rougher particles. Roughness reduces the transverse diffusivities relative to smoother particles for sufficiently concentrated suspensions of frictionless and low-friction particles. However, the diffusivity of roughened particles is larger than smoother ones at high values of the friction coefficient. The increase of the diffusivity with friction is associated with a significant broadening of the variance of the rotational velocities. The most prevalent observation, when correlating the microstructure to changes in diffusivity for frictionless particles, is that less diffusive systems, with larger roughness, form layers along the flow direction. These results confirm previous experimental and simulation results that roughness can decrease diffusivity at large concentrations using a more detailed model. Also, comparisons of the simulation results with previously published experimental measurements indicate that friction improves the alignment of the results with experiments.