Irregularities on the outer surface of Inertial Confinement Fusion (ICF) capsules accelerated by laser irradiation are amplified by the Rayleigh–Taylor instability (RTI), which occurs at the ablation front (ablative RTI), where density gradient and acceleration have the same direction. The analytic stability theory of subsonic ablation fronts, for Froude number larger than one, shows that the main stabilization mechanisms are blowoff convection (rocket effect equilibrating the gravity force) and ablation (Sanz 1994; Betti et al. 1996). Blowoff convection and ablation are enhanced if the ablator material is mixed with high-Z dopants. The latest enhances radiation emission setting the ablator on a higher adiabat, lowering its density, and increasing the ablation velocity. When such an ablator is used to push a solid deuterium-tritium (D–T) shell, the D–T-ablator interface becomes classically unstable. The aim of this paper is to investigate the stability of such a configuration, represented by a low-density ablator pushing a heavier shell, and study the interplay between the classical and ablative RTIs occurring simultaneously. The stability analysis is carried out using a sharp boundary model (Piriz et al. 1997), which contains all the basic physics of the RTI in ICF.