This study explores the fire behavior of wood–glass and jute–glass hybrid laminates, with a focus on the influence of jute and wood veneers as new materials for composite production. Five-layer hybrid laminates were manufactured using the vacuum infusion process (VIP). Combustion and carbonization performances were assessed using a cone calorimeter based on the ISO 5660 method. This study evaluates flammability through key parameters including ignition time, heat release rate, and smoke production. The results indicated that the ignition time was significantly longer (ca. 64 s) for the glass–jute laminate (GJGJG), compared to the wood–glass laminate (WGWGW) (ca. 53 s). The heat release rate of laminates containing organic components was higher than the sample composed only of glass mat (G5) but their rates were all lower than the polyester reference resin. WGWGW, compared to the GJGJG sample, was able to produce a good-quality protective shield and, therefore, postpone the occurrence of the heat release peak. In this way, the fire growth rate index (FIGRA) best performance was accomplished by the WGWGW sample (2.7 ± 0.3 kW/m2 × s), which was even better than that of the G5 sample. The total-smoke-released value was highest for polyester, 7361 ± 839 m2/m2, followed by WGWGW, 2873 ± 188 m2/m2, and J5, 2484 ± 216 m2/m2. Among the hybrid laminates, the best performance was obtained by GJGJG, 1860 ± 49 m2/m2, but compared to the G5 laminates, it was only ~36% higher. The specific extinction area (SEA) is a smoke parameter related to the mass of the samples; the best result was obtained by WGWGW with 697 ± 31 m2/kg. Finally, the neat polyester and all laminates achieved UL 94HB classification, with firing rates below 40 mm/min.