Composite laminate recycling and waste disposal routes remain a burden to existing systems, requiring special treatment and separation. The inclusion of a plastic layer is important for several key properties that are required for food safety, which in turn has made these products exceptionally hard to substitute in food packaging. Yet, the continued use of non-degradable commodity plastics is unsustainable. In this research, we compare the four most promising biodegradable and bio-based plastics that could replace non-degradable plastics in laminates. Polyhydroxyalkanoate (PHA), polylactic acid (PLA), polybutylene succinate (PBS), and polybutylene succinate adipate (PBSA) were applied as a direct melt coating on porous cast hemp papers, and the final composite was compressed under three different loads: 0.5 MT, 1.5 MT, and 3.0 MT. To promote sustainable agriculture waste management, we opted to use cast paper made from ground hemp stalks. The formation of the composite structure was examined with scanning electron microscopy (SEM), while surface wetting on the paper side of the laminate was performed to understand structural changes induced by polymer impregnation into the paper layer. Mechanical performance properties were investigated with tensile and peel tests, and suitability for an extended range of temperatures was examined with dynamical mechanical analysis. An increase in compression pressure yielded up to a two-fold improvement in elastic modulus and tensile strength, while thermomechanical analysis revealed that the polymer’s transition into a viscoelastic state significantly affected the laminate’s storage modulus values. Biodegradation was performed in a controlled compost at 58 °C, resulting in full degradation within 40 to 80 days, with PLA and PHA laminates showing 40 and 50 days, respectively. Produced bioplastic laminates have a tremendous potential to replace polyolefin laminates in packaging applications.