The effect of polydispersity on the width of the interphase between an end-tethered polymer and a polymeric matrix has been investigated using a computer program which solves a self-consistent field model of a polymer chain distributed on a cubic lattice. This model was used to calculate an average volume fraction of each species along the axis perpendicular to the grafting plane. A Flory-Huggins-type expression, generalized to a multicomponent system, was used to model the free-energy change of mixing. The logarithmic-normal molecular weight distribution function was employed to generate the desired molecular weight distribution for the end-tethered polymer while the matrix was assumed to be monodisperse. Brushes having polydispersities from 1.0 (monodisperse) to 3.0 were studied under repulsive, attractive, and athermal enthalpic brush-matrix interactions. The effect of polydispersity on the width of the interphase was found to be dependent upon the type of enthalpic interaction. When a repulsive brush-matrix interaction existed, the width of the interphase was not affected by brush polydispersity; however, the brush profile showed evidence of an increased stretching of the brush into the matrix as the polydispersity was increased from 1.0 to 3.0 with the attractive and athermal interactions, indicating enhanced mixing in the interphase. The use of polydisperse brushes at solid-polymer interfaces for adhesion promotion is discussed by considering how enhanced brush-matrix contact and a surface exclusion zone affect the interfacial toughness.