Low-energy (100 eV) electron-stimulated reactions in layered H2O/CO/H2O ices are investigated. For CO layers buried in amorphous solid water (ASW) films at depths of 50 monolayers (ML) or less from the vacuum interface, both oxidation and reduction reactions are observed. However, for CO buried more deeply in ASW films, only the reduction of CO to methanol is observed. Experiments with layered films of H2O and D2O show that the hydrogen atoms participating in the reduction of the buried CO originate in the region that is 10-50 ML below the surface of the ASW films and subsequently diffuse through the film. For deeply buried CO layers, the CO reduction reactions quickly increase with temperature above ∼60 K. We present a simple chemical kinetic model that treats the diffusion of hydrogen atoms in the ASW and sequential hydrogenation of the CO to methanol to account for the observations.