Due to the versality, surface imperfections and diverse redox chemistry of CuxS, hybrid ion exchangers (HIXs) containing these particles are an interesting object of research, including thermal transformation. The composite materials used for testing were strongly basic anion exchangers, with macroreticular (M) and gel-type structure (G), containing in the poly (styrene/divinylbenzene) skeleton fine particles of covellite/brochantite (M1), covellite (M2), covellite/digenite/djurleite (G1) and covellite/digenite (G2). The prepared HIXs contained 12–16 mass% S + Cu. They were subjected to thermal analysis under air and N2 to identify the role of the inorganic phase in decomposition of the polymeric phase. The results were discussed on the basis of the TG/DTG curves and X-ray diffraction (XRD) patterns of the solid residues (CuO after combustion, carbon/Cu2S after pyrolysis). It was found that CuxS in the resin phase exhibited oxidative activity promoting the combustion process. The polymeric skeleton of HIXs decomposed in air at a much lower temperature compared to pure resins (400 vs 600 °C). The TG/DTG curves had a model shape, three separate conversions occurring in a narrow temperature range, which indicated sequential decomposition. The low consumption of hydrogen for the reduction of CuxS to Cu2S during pyrolysis was not conducive to condensation of alkyl radicals and increase of the mass of carbon matter. The results advance the understanding of the effect of copper/sulfur-containing fine particles on the thermal decomposition of anion exchanger and can be useful in preparation of multifunctional carbon-containing composite materials.