La1.5Sr0.5CoMn0.5Fe0.5O6 (LSCMFO) compound was prepared by solid state reaction and its structural, electronic and magnetic properties were investigated. The material forms in rhombohedral R3 structure, and the presence of distinct magnetic interactions leads to the formation of a Griffiths phase above its FM transition temperature (150 K), possibly related to the nucleation of small short-ranged ferromagnetic clusters. At low temperatures, a spin glass-like phase emerges and the system exhibits both the conventional and the spontaneous exchange bias (EB) effects. These results resemble those reported for La1.5Sr0.5CoMnO6 but are discrepant to those found when Fe partially substitutes Co in La1.5Sr0.5(Co1-xFex)MnO6, for which the EB effect is observed in a much broader temperature range. The unidirectional anisotropy observed for LSCMFO is discussed and compared with those of resembling double-perovskite compounds, being plausibly explained in terms of its structural and electronic properties.