In this study, polybutylene succinate was melt blended with polypropylene (PP) to fabricate partially bio-based and miscible composites filled with various loading silicon nitride (Si3N4) particles. Oleic acid and PP-grafted maleic anhydride were used as a functionalizing agent for Si3N4 and as a compatibilizer for polymer blends, respectively. The surface functionalization of the Si3N4 particles enhanced the interfacial adhesion between the filler and the blended polymers, affecting the thermal and mechanical properties of the composites. The thermal conductivity of the composite filled with only 18.6 vol% surface-treated Si3N4 increased by 342% compared to that of the blended polymer. In addition, the surface treatment of Si3N4 significantly improved the Young’s modulus, tensile strength, and thermal stability of the corresponding composites. However, the temperature-dependent storage modulus was unaffected by the surface treatment of Si3N4 and increased as the loading content of the Si3N4 particles increased.