Hydrogen can be produced from reduction of water at the cathode of a solid oxide electrolysis cell (SOEC) and electricity and CO gas can be co-generated from the oxidation of carbon at the anode of a direct carbon solid oxide fuel cell (DC-SOFC). In the present work, a solid oxide cell (SOC) combining the cathode reaction of the SOEC and the anode reaction of the DC-SOFC is proposed, prepared, and investigated. It is demonstrated that hydrogen and CO can be separately produced from the cathode and anode through simultaneous reduction of water and oxidation of carbon in such a H2O-C SOC. Resistances from electrode polarizations are analyzed through measuring current-voltage characteristics, overpotentials, and AC impedances of the cell. The advantage of the H2O-C SOC over two separately operated SOEC and DC-SOFC is verified by the resistance analysis. An electrolyte-supported H2O-C SOC, with a cermet of silver and gadolinium-doped ceria (Ag-GDC) as the symmetrical electrode material and a steam concentration of 50 % at the cathode, gives an operating current density of 0.67 A cm-2 at the thermal neutral voltage (0.7 V). It stably operates at 0.2 A cm-2 under an applied voltage of only 0.16 V, producing pure hydrogen from the cathode and CO with a concentration of 88 % from the anode. The performance is significantly improved by using an anode-supported H2O-C SOC which gives an operating current density of 2.27 A cm-2 at the thermal neutral voltage.