The aim of this work is to study the instability of interacting waves between two immiscible magnetic liquids. The effects of gravitation and a uniform normal magnetic field are taken into account. The method of multiple scales is used to determine the stability criteria of the considered problem. The various stability criteria are discussed both analytically and graphically. According to the numerical examples, we have remarked that the increase of the ratio of the permeability of the liquids appears to be the destabilizing effect of the magnetic field. The short waves below the critical wavenumbers are stable whereas a number of long waves are unstable. The viscosity effect on the stability criteria is a dual-role one, depending on the strength of the applied magnetic field.