The linear stability of the Poiseuille flow of multi-layered different fluids, described mathematically by a system of Orr-Somerfeld differential equations, is investigated. A spectral method is used to rewrite this system into a generalized eigenvalue problem, which can be solved with the QZ-algorithm. Special attention is paid to the tractibility of the interfacial conditions of the stability problem. Since we will limit ourselves to a linear stability analysis, the analytical treatment of the interfacial conditions is simplified. Some results related to simple flow configurations are presented. The origin of certain regions of interfacial instability is explained by simple analytical reasoning.