The physics of diffusion phenomena in nano- and microchannels has attracted a lot of attention in recent years, due to its close connection with many technological, medical, and industrial applications. In the present paper, we employ a kinetic approach to investigate how the confinement in nanostructured geometries affects the diffusive properties of fluid mixtures and leads to the appearance of properties different from those of bulk systems. In particular, we derive an expression for the friction tensor in the case of a bulk fluid mixture confined to a narrow slit having undulated walls. The boundary roughness leads to a new mechanism for transverse diffusion and can even lead to an effective diffusion along the channel larger than the one corresponding to a planar channel of equivalent section. Finally, we discuss a reduction of the previous equation to a one dimensional effective diffusion equation in which an entropic term encapsulates the geometrical information on the channel shape.