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We present the structural, electronic, and magnetic properties of BaMn₂Sb₂ and Ba₂Mn₃Sb₂O₂ single crystals, both with the layered structure analogous to high-temperature Fe- and/or Cu-based superconductors. While the Mn moment in the MnSb₄ tetrahedral environment forms a long-range G-type antiferromagnetic (AFM) ordering in both BaMn₂Sb₂ (T_N1 ≈443 K) and Ba₂Mn₃Sb₂O₂ (T_N1 ≈314 K), a short-range AFM order is found in the intercalated MnO₂ layer at a much lower temperature (T_N2 ≈60 K) coexisting with long-range G-type order in MnSb₄ layer in Ba₂Mn₃Sb₂O₂. The directions of the ordered moments in these two magnetic sub-lattices of Ba₂Mn₃Sb₂O₂ are perpendicular to each other. The G-type AFM order in MnSb₄ layers in both compounds is distinct from the stripe-like order in Fe-based superconductors, but the in-plane magnetic structure in MnO₂ layers of Ba₂Mn₃Sb₂O₂ is found to be similar to that in the Cuprates. Our study reveals the significant and distinct roles of the CuO₂- and FeAs₄-type transition metal layers in the structure, novel magnetic and electronic properties.