Collisional plasma shocks generated from supersonic flows are an important feature in many astrophysical and laboratory high-energy-density plasmas. Compared to single-ion-species plasma shocks, plasma shock fronts with multiple ion species contain additional structure, including interspecies ion separation driven by gradients in species concentration, temperature, pressure, and electric potential. We present time-resolved density and temperature measurements of two ion species in collisional plasma shocks produced by head-on merging of supersonic plasma jets, allowing determination of the diffusion velocity of the ion species. Our results demonstrate that the lighter ion species diffuse faster than the heavier species within a shock front, consistent with predictions from the interion-species transport theory. Results from the experiment approach quantitative agreement with theoretical prediction and 1D ion-Fokker-Planck kinetic simulation.