Tissue engineering is an interdisciplinary field that develops new methods to enhance the regeneration of damaged tissues, including those of wounds. Polymer systems containing bioactive molecules can play an important role in accelerating tissue regeneration, mitigating inflammation process, and fighting bacterial infection. Chitosan (CS) has attracted much attention regarding its use in wound healing system fabrication thanks to its biocompatibility, biodegradability, and the presence of functional groups in its structure. In this work, bioactive chitosan-based membranes were obtained by both chemical and physical modifications of the polymer with glycidyl methacrylate and glycerol (GLY), respectively. The most suitable GLY concentration to obtain wound healing systems with good elongation at break, a good water vapor transmission rate (WVTR), and good wettability values was 20% (w/w). Afterwards, the membranes were crosslinked with different concentrations of ethylene glycol dimethacrylate (EGDMA). By using a concentration of 0.05 mM EGDMA, membranes with a contact angle and WVTR values suitable for the application were obtained. To make the system bioactive, 3,4-dihydrocinnamic acid (HCAF) was introduced into the membranes, either by imbibition or chemical reaction, using laccase as a catalyst. Thermal and mechanical analyses confirmed the formation of a cohesive network, which limited the plasticizing effect of GLY, particularly when HCAF was chemically bound. The HCAF-imbibed membrane showed a good antioxidant and antimicrobial activity, highlighting the potential of this system for the treatment of wound healing.