The structural properties of nonuniform, binary, sticky hard-sphere (SHS) fluid mixture (the particular components being denoted by SHS1 and SHS2) within a planar pore, maintaining the equilibrium with the bulk phase, were investigated. The wall-SHS1 and wall-SHS2 correlations of the SHS mixture confined in the pore, and its distribution between the pore and the bulk phase were studied on the basis of the solution to the Percus-Yevick/Ornstein-Zernike equation, obtained by using the analytic results for the direct correlation functions of the bulk SHS mixture. The density profiles of particular components with the hard core diameters sigma (1) and sigma (2) revealed distinct layering, a characteristic feature being the discontinuities in the slopes of the profiles at the distances n.sigma (1)+m.sigma (2) (n=0,1,...;m=0,1,...) from the wall-SHS1 and wall-SHS2 contact planes. It was shown that narrowing of the pore considerably affects the partitioning of both components between the bulk phase and the interior of the pore, the effects being more pronounced in the case of a more adhesive component. As the individual components of the binary mixture are selectively partitioned between the bulk phase and narrow pore, the porous material, i.e., a network of narrow pores, makes possible a partial separation of both components from the bulk SHS mixture.