In this study, the mechanical behavior of aluminum honeycomb (AHC) sandwich structures filled with ethylene vinyl acetate copolymer (EVA) foam in situ under out-of-plane compression loading was investigated experimentally. Both non-filled and EVA-foam-filled sandwich specimens with three different AHC core cell sizes (5.20, 6.78, and 8.66 mm) were studied to correlate the foam-filling effect with a key structural parameter. The results showed that compression characteristic properties such as peak stress, plateau stress, and absorbed energy per unit volume of the sandwich structure increased with EVA foam filling. The structure showed high recoverability when the compression loading was removed due to the viscoelastic nature of EVA foam. Cored EVA sandwich with 8.66 mm AHC cell size was recovered at 44% of the original thickness. This result promises groundbreaking applications such as impact-resistant and self-healing structures. The microstructures were also observed using scanning electron microscopy (SEM) to investigate the failure and the recoverability mechanisms.