We theoretically investigate the nonreciprocal optical response of a one-dimensional multilayer possessing nonlinear (NL) Kerr dielectrics hybridized with a VO2-based core–shell structure. As a consequence of parameter optimization, it is found that semiconductor-to-metallic reconfiguring of relatively thin VO2 nanoinclusions with a core–shell radius ratio of 0.95 is accompanied by enhanced multispectral near-infrared absorption of the system for both forward and backward incidences of light.However, increasing intensity of the incident wave bends the resonant wavelengths due to the NL response of Kerr dielectrics. When the incident light is well set up for an appropriate non-resonant wavelength, the absorption contrast between two directions of incidence enhances in some ranges of intensities due to the NL Kerr effect. There is also the possibility of reaching S-shaped bistable absorption. These features make the modeled system suitable for designing near-infrared absorptive diodes or isolators.