The properties of structural planes and the strength of rock matrix significantly influence the splitting characteristics of composite rock masses. To investigate the effects of structural plane and differences in matrix strength on the mechanical behavior and failure characteristics of composite jointed rock bodies, composite jointed disc specimens with varying structural plane roughness and matrix combinations were prepared. These specimens were then subjected to Brazilian split tests under different loading angles ranging from 0° to 90°. Results indicate that the failure mode of the specimens is determined by the angle of the structural plane. As the structural plane angle increases, the failure mode transitions from structural plane failure to combination failure and finally back to structural plane failure. Increased roughness of the structural plane reduces the extent of structural plane failure, while matrix strength has no significant impact on the failure mode. The failure load of the specimens increases with increasing structural plane angle, roughness, and matrix strength. The influence of structural plane roughness and matrix strength on the mechanical properties of the specimens grows with increasing structural plane angle. Increases in structural plane roughness and matrix strength significantly enhance the strain energy and dissipated energy of the disc model. Finally, an analysis of the stress state on the structural planes is combined with an exploration of the failure mechanisms of the specimens.