A self-consistent density-functional approach is developed for the structure of nonuniform fluid mixtures, where the second-order direct correlation function and the bridge function of the corresponding uniform fluid mixture are used as the input. These two quantities are obtained through integral equation theory using an accurate closure relation. The present theory uses the concept of universality of the free energy density functional to obtain the first-order direct correlation function of the nonuniform system from that of the corresponding uniform system. This new approach is employed to predict the structure of binary hard-sphere fluid mixtures near a hard wall. The calculated density and concentration profiles are shown to compare well with available computer simulation results.