We have investigated the structure and magnetic properties of the perovskite oxides of the formula La₂Fe$_{1-x}$Mn$_{2x}$Cr$_{1-x}$O₆ ($0 < x < 1.0$). For $0 < x ≤ 0.5$, the members adopt the orthorhombic (Pbnm) structure, where the transition metal atoms are disordered at the 4b sites and the MO₆ (M = Fe, Mn, Cr) octahedra become increasingly distorted with increasing 𝑥. For $0.65 ≤ x < 1.0$, the members adopt the rhombohedral (R-3c) structure that is similar to LaMnO$_{3+\delta}$ ($\delta ≥ 0.1$) where the MO₆ octahedra are undistorted. While the magnetic properties of the latter series are largely similar to the parent LaMnO$_{3+\delta}$ arising from the double-exchange (DE) between mixed valent Mn^III/Mn^IV, the magnetic properties of the orthorhombic members show a distinct (albeit weak) ferromagnetism ($T_C \sim 200$ K) that seems to arise from a Mn^III-mediated superexchange (SE) between Fe^III/Cr^III in the disordered perovskite structure containing Fe^III, Mn^III and Cr^III.