Interfacial instability of two layers of thin (< 100-nm) immiscible liquid films on a solid substrate is studied using the long-wave equations. Instability is derived from the van der Waals interactions among the substrate and the films. The stability characteristics are classified on the basis of the different combinations of surface tensions of the liquid layers and the solid. Depending on the surface tensions and the film thicknesses, two distinct modes of instability, namely, squeezing and bending, are manifested. Nonlinear simulations are presented to describe the various modes of initial evolution and film rupture in such systems.