An unpolarized normal-incidence light beam reflected by a cholesteric liquid crystal is left- or right-circularly polarized, in the cholesteric temperature range. In this article, we present a novel approach for fabricating a cholesteric liquid crystalline material that exhibits reflection bands with both senses of polarization at room temperature. A cholesteric liquid crystal that presents a twist inversion at a critical temperature T-c is blended with a small quantity of photopolymerizable monomers. Upon ultraviolet irradiation above T-c, the liquid crystal becomes a polymer-stabilized liquid crystal. Below T-c, the material reflects a dual circularly polarized band in the infrared. By quenching the experimental cell at a temperature below the blend's melting point, the optical properties of the material in an undercooled state are conserved for months at room temperature, which is critical to potential applications such as heat-repelling windows and polarization-independent photonic devices.