The pulse duration dependence of single-shot laser-induced damage and ablation of HfO2/SiO2-based double- and quadlayer thin films is studied using time-resolved surface microscopy (TRSM) and ex situ imaging down to the few-cycle pulse (FCP) regime. Both samples exhibit a raised, "blister" morphology for a range of fluences between the damage and ablation thresholds. The fluence range associated with blister formation is much larger for FCPs than for 110 fs pulses, and TRSM images at early time-delays show that the density of the laser-generated plasma is much higher for 110 fs pulses for a lower fluence relative to the damage threshold. Also, for high enough fluences the excited electron density exhibits a fast decay down to a significantly high value, which remains even after the onset of mechanical damage of the layers. The pulse duration dependence suggests that as fluence is increased, the increase in absorbed energy is more gradual for FCPs, which points towards inherent differences in the way high intensity FCPs are absorbed in dielectrics relative to longer femtosecond laser pulses.