We theoretically investigate the steady-state bistable intersubband polariton response of quantum-well (QW) structures embedded into planar semiconductor microcavity to intense plane wave incident radiation. A rigorous semiclassical approach employs the transfer matrix formalism and the sheet model, which includes the dynamic depolarization effect. Results of comprehensive numerical simulations on reflectance characteristics of the structures with strong coupling between the ground cavity mode of the electromagnetic field and intersubband excitations in QWs are presented. The mechanism of the polariton-based optical bistability (OB) is revealed. Both the mirror-based optical bistability (MOB) and the intrinsic optical bistability (IOB) are investigated, with the focus on the MOB. Polariton-based bistabilities driven by cyclically changing intensity of the incident radiation, frequency of the incident radiation, and the angle of incidence are considered. It is found that the presence of the dynamic depolarization effect brings novel features to the OB reflectance characteristics of the structures. Effect of accumulation of the MOB cooperativity parameter is revealed. The concept of effective QW is proposed to describe a tremendously enhanced MOB response of multiple identical QWs particularly located in the cavity. A remarkable possibility of MOB in systems of multiple particularly located QWs with big values of dephasing rate is demonstrated. It is shown that the transition from bistability to multiple bistability and to multistability for two QWs can be controlled by slight manipulation of the angle of incidence. A possibility is found for an outstanding width of the hysteresis of the angular-domain OB, being about one degree.