The purpose of this paper was to examine the possibility of producing new blends of hydrogenated acrylonitrile-butadiene and chloroprene rubbers (HNBR/CR) unconventionally cross-linked with silver(I) oxide (Ag2O), and to investigate the physicomechanical properties of the obtained materials. From the obtained results, it can be concluded that HNBR/CR composites were effectively cured with Ag2O, which led to interelastomer reactions, and the degree of binding of HNBR with CR was in the range of 14–59%. The rheometric and equilibrium swelling studies revealed that the cross-linking progress depended on the weight proportion of both elastomers, and the degree of cross-linking was greater with more content of chloroprene rubber in the tested blends. Interelastomer reactions occurring between HNBR and CR improved the homogeneity and miscibility of the tested compositions, which was confirmed by differential scanning calorimetry (DSC) and scanning electron microscopy (SEM) analyses. The tensile strength and hardness of the obtained HNBR/CR/Ag2O vulcanizates proportionally increased with the content of CR, while the tear strength showed an inverse relationship. The obtained new, unconventional materials were characterized by significant resistance to thermo-oxidative factors, which was confirmed by the high aging factor.