This study employed a hydrogen atmosphere in an analytical reactor to investigate the thermochemical transformation of Chilean Oak (ChO) and polyethylene. Thermogravimetric assays and compositional analyses of the evolved gaseous chemicals provided valuable insights regarding the synergistic effects during the co-hydropyrolysis of biomass and plastics. A systematic experimental design approach assessed the contributions of different variables, revealing the significant influence of the biomass/plastic ratio and hydrogen pressure. Analysis of the gas phase composition showed that co-hydropyrolysis with LDPE resulted in lower levels of alcohols, ketones, phenols, and oxygenated compounds. ChO exhibited an average oxygenated compound content of 70.13%, while LDPE and HDPE had 5.9% and 1.4%, respectively. Experimental assays under specific conditions reduced ketones and phenols to 2–3%. Including a hydrogen atmosphere during co-hydropyrolysis contributes to enhanced reaction kinetics and reduced formation of oxygenated compounds, indicating its beneficial role in improving reactions and diminishing the production of undesired by-products. Synergistic effects were observed, with reductions of up to 350% for HDPE and 200% for LDPE compared to the expected values, achieving higher synergistic coefficients with HDPE. The proposed reaction mechanism provides a comprehensive understanding of the simultaneous decomposition of biomass and polyethylene polymer chains, forming valuable bio-oil products and demonstrating the how the hydrogen atmosphere modulates and influences the reaction pathways and product distribution. For this reason, the co-hydropyrolysis of biomass–plastic blends is a technique with great potential to achieve lower levels of oxygenated compounds, which should be further explored in subsequent studies to address scalability and efficiency at pilot and industrial levels.