The simultaneous encapsulation of drugs into nanosized delivery systems could be beneficial for cancer therapies since it could alleviate adverse reactions as well as provide synergistic effects. However, the encapsulation of hydrophobic drugs into hydrophilic nanoparticles, such as nanogels, could be challenging. Therefore, innovative technological approaches are needed. In this research, a composite nanogel system was prepared from chitosan, albumin, and hydroxypropyl-β-cyclodextrin for co-delivery of the hydrophilic anticancer drug doxorubicin and hydrophobic antioxidant resveratrol. The nanoparticles were characterized using dynamic light scattering and found to have a hydrodynamic diameter of approx. 31 nm, narrow size distribution (PDI = 0.188), positive ƺ-potential (+51.23 mV), and pH-dependent release of the loaded drugs. FTIR and X-ray analyses proved the successful development of the composite nanogel. Moreover, the double-loaded system showed that the loading of resveratrol exerted protection against doxorubicin-induced toxicity in cardioblast H9c2 and neuroblast SH-SY5Y cells. The simultaneous loading did not influence the cytostatic effect of the antitumor agent in lymphoma L5178Y and L5178MDR cell lines.