We report flow statistics from simulations using the direct simulation Monte Carlo method for turbulent Couette flow where the lower wall is replaced by an idealized rough surface. We focus on conditions yielding a modest global Reynolds number, supersonic Mach number, and a global Knudsen number in the near-continuum regime, allowing for comparison with direct numerical simulation of the Navier-Stokes equations for the same conditions. While we observe discrepancies on the order of a few percent, we find the overall level of agreement between macroscopic and molecular-level descriptions of turbulent flow encouraging.