La$_{1.5}$Sr$_{0.5}$CoMn$_{0.5}$Fe$_{0.5}$O$_{6}$ (LSCMFO) compound was prepared by solid state reaction and its structural, electronic and magnetic properties were investigated. The material forms in rhombohedral $Rbar{3}c$ 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 La$_{1.5}$Sr$_{0.5}$CoMnO$_{6}$ but are discrepant to those found when Fe partially substitutes Co in La$_{1.5}$Sr$_{0.5}$(Co$_{1-x}$Fe$_{x}$)MnO$_{6}$, 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.