In this work, renewable composites were prepared by the association of a thermosetting resin synthesized via free-radical polymerization, using a mixture of tung oil, n-butyl methacrylate, and divinylbenzene, with silica-rich fillers, namely an algae biomass with high silica content, and a well-sorted sand. Furthermore, to investigate if the interaction between the non-polar resin and polar reinforcements could be improved, enhancing the materials’ mechanical properties, itaconic anhydride, a bio-derived molecule obtained from itaconic acid, was introduced to the resin composition. Thermogravimetric analysis (TGA) suggested that the thermal stability of the composites was overall not changed with the addition of itaconic anhydride. The mechanical properties of the sand composites, however, did improve, as the storage modulus at room temperature, measured by dynamic mechanical analysis (DMA), almost doubled in the presence of itaconic anhydride. The glass transition temperatures of the materials increased by approximately 30 °C when sand was used as a reinforcement. Water absorption experiments validated an increase in the polarity of the unreinforced resin by the addition of itaconic anhydride to its formulation. The composites, however, did not exhibit a significant difference in polarity in the presence of itaconic anhydride. Finally, scanning electron microscopy (SEM), equipped with energy dispersive spectroscopy (EDS), demonstrated better matrix–filler adhesion in the presence of itaconic anhydride for high-silica algae composites.