A newly developed self-consistent formulation of the polymer reference interaction site model (PRISM) theory is used to predict the structure of binary polymer blends. Theoretical radial distribution functions are compared to those obtained from hybrid Monte Carlo simulations of mixtures of Lennard-Jones chains. A multiple time step method is implemented to increase the efficiency of the simulations. We examine both the cases of atomic and molecular closures and consider both conventional and self-consistent PRISM. We find that, overall, theoretical distribution functions are in good agreement with simulation.