A wide range of naturally derived and synthetic biodegradable and biocompatible polymers are today regarded as promising materials for improving skin regeneration. Alongside this, these materials have been explored in conjunction with different types of antimicrobial and bioactive agents, especially natural-derived compounds, to enhance their biological properties. Herein, a double-layered nanocomposite dressing membrane was fabricated with two distinct layers. A bottom layer from Chitosan-Sodium tripolyphosphate (CS-TPP) and Poly(vinyl alcohol) (PVA) containing Centella asiatica (L.) (CA) was electrospun directly over a Polycaprolactone (PCL) layer to improve the biologic performance of the electrospun nanofibers. In turn, the PCL layer was designed to provide mechanical support to the damaged tissue. The results revealed that the produced double-layered nanocomposite membrane closely resembles the mechanical, porosity, and wettability features required for skin tissue engineering. On the other hand, the in vitro drug release profile of the PCL/PVA_CS-TPP containing CA exhibited a controlled release for 10 days. Moreover, the PVA_CS-TPP_CA’s bottom layer displayed the highest antibacterial activity against Staphylococcus aureus (S. aureus) (99.96 ± 6.04%) and Pseudomonas aeruginosa (P. aeruginosa) (99.94 ± 0.67%), which is responsible for avoiding bacterial penetration while endowing bioactive properties. Finally, the 3-(4,5-Dimethyl-2-thiazolyl)-2,5-diphenyl-2H-tetrazolium bromide (MTT) assay showed that this nanocomposite membrane was not cytotoxic for normal human dermal fibroblasts (NHDF) cells. Therefore, these findings suggest the potential use of the double-layered PCL/PVA_CS-TPP_CA as an efficient bionanocomposite dressing material.