Interdiffusion in polymer bilayers of polystyrene (PS) and the statistically random copolymer poly(styrene-r-4-bromostyrene) (PBS), (C8H(8-x)Brx)(N), -here x is the mole fraction of brominated repeat units in the copolymer and N the degree of polymerization, was studied using Rutherford backscattering spectroscopy (RBS). PS/PBS bilayers with 0.04 < x < 0.63 and the ratio N-PS/N-PBS varied from 0.06 < N-PS/N-PBS < 18.1 were examined. PBS volume fraction versus depth profiles were obtained from the evolution of the bromine peak in the RBS spectra. It is shown that as the phase boundary is approached, interdiffusion occurs until layer compositions indicative of binodal conditions are reached. These observations are in very good agreement with phase diagrams obtained using Flory-Huggins theory and a PS/PBS interaction parameter measured using small angle X-ray scattering. For N-PS/N-PBS not equal 1, the mobility is dictated by the faster diffusing (lower N) component, resulting in an interface which moves toward the faster diffusing component. This result is consistent with fast mode theory; equilibrium conditions correspond to the asymmetry of the phase diagrams. Mutual diffusion coefficients were determined by comparison of the RBS data to a mean-field interdiffusion model using the fast mode expression for mobility. The mutual diffusion coefficient is shown to decrease with increasing N and x and increase with temperature. The implications of this miscibility dependence of the interdiffusion behavior, based on both composition of the copolymer and degree of polymerization, are discussed in the context of strengthening homopolymer/random copolymer interfaces.