On the basis of the Mn(3+) for Fe(3+) substitution in Pb(2-x)Ba(x)Fe2O5, a novel oxide Pb1.3Ba0.7MnFeO5 has been synthesized at normal pressure. Though it belongs to the same structural family, the mixed "MnFe" oxide exhibits a very different structural distortion of its framework compared to the pure "Fe2" oxide, due to the Jahn-Teller effect of Mn(3+). Combined neutron diffraction, high resolution electron microscopy/high angle annular dark field-scanning transmission electron microscopy (HAADF-STEM) investigations allow the origin of this difference to be determined. Here we show that the MO6 octahedra of the double perovskite layers in the "MnFe" structure exhibit a strong tetragonal pyramidal distortion "5 + 1", whereas the "Fe2" structure shows a tetrahedral distortion "4 + 2" of the FeO6 octahedra. Similarly, the MO5 polyhedra of the "MnFe" structure tend toward a tetragonal pyramid, whereas the FeO5 polyhedra of the "Fe2" structure are closer to a trigonal bipyramid. Differently from the oxide Pb(2-x)Ba(x)Fe2O5, which is antiferromagnetic, the oxide Pb1.3Ba0.7MnFeO5 exhibits a spin glass behavior with Tg ∼ 50 K in agreement with the disordered distribution of the Mn(3+) and Fe(3+) species.