A polycrystalline oxygen-stoichiometric La2ZnMnO6 double-perovskite oxide has been prepared by soft-chemistry procedures, followed by annealing in air at 800°C. A reduced specimen, with a La2ZnMnO6−δ composition, has been obtained by topotactical oxygen removal in an H2/N2 (5%/95%) flow at 600°C. The structural characterization has been conducted from neutron powder diffraction (NPD) data, very sensitive to the contrast between Zn and Mn and the oxygen stoichiometry. Both perovskites (oxidized and reduced) crystallize in the monoclinic P21/n space group, exhibiting an antisite Zn/Mn disorder of about 15% and 14%, respectively. The partial reduction of Mn4+ to Mn3+ in the reduced phase is accompanied with the occurrence of oxygen vacancies, located at the axial octahedral sites. Thermogravimetric analysis (TGA) substantiates the oxygen stoichiometry and the stability range. Magnetic susceptibility measurements indicate an antiferromagnetic behaviour, confirming the presence of Mn3+ ions in the structure. The magnetic structure of the reduced phase, determined from NPD data at 3 K, shows an antiferromagnetic G-type coupling between Mn at 2c and 2d sites (promoted by the anti-site disorder); the ordered magnetic moment at Mn site is 0.789 μB at 3 K. Both phases display a semiconductor-like behaviour with a maximum conductivity of 0.052 S∙cm−1 for the reduced phase at 650 °C, due to the occurrence of Mn3+-Mn4+ mixed valence. Moreover, the measured thermal expansion coefficients perfectly match with the values usually displayed by SOFC electrolytes. The reversibility and versatility of the present compounds as catalysts for oxygen reduction (cathode) or fuel oxidation (anode) were tested in single SOFC cells yielding power density spanning from 120 to 155 W/cm2 using these perovskites as anode, cathode and symmetric electrodes for SOFC.