A modified density functional theory is proposed to describe fluid adsorption and absorption by a solid, the density of which is nonhomogeneous near the interface. The density distribution of the solid is not provided by apriori assumptions, but is obtained via the minimization of an appropriate thermodynamic potential. The theory considers a mixture of two components in a slitlike pore. One of them, the fluid, is in contact with a reservoir containing the same kind of molecules and can be described through a grand canonical ensemble. The other component has strong interactions between its molecules. As a consequence, it forms a solid in the slit which can be treated as a canonical ensemble of a fixed number of molecules. The theory predicts both an intrinsic (in the absence of fluid) change in the solid density near the interface and a solid density variation as the fluid density in the reservoir is changed. In addition, it reveals that the oscillations that occur in the fluid density when the solid density is uniform are damped by the nonuniform solid. The theory provides the amounts of fluid adsorbed as well as absorbed by the solid.