Proton ceramic fuel cells are promising electrochemical converters that produce electrical energy by oxidizing hydrogen. Understanding the impact of gas humidification on the characteristics of such fuel cells is pivotal for the development of high-performance devices. This study develops a theory elucidating the effect of hydrogen and air humidity on the output characteristics of fuel cells based on proton-conducting oxide membrane with mixed (proton and hole) conductivity. The theory is based on a self-consistent description of the strong non-uniform distribution of charge carriers inside the membrane and the variation of the gas phase composition along the fuel and air channels. It is shown that the total current density significantly and nontnonotonously depends on humidity of the inlet hydrogen fuel, while humidification of the inlet air has minor effect on the fuel cell characteristics. The influence of the anode and cathode gas humidity on the distribution of the various fuel cell parameters (current densities, resistivity, etc.) along the membrane is also determined. The obtained results reveal the possibility of enhancing the performance of the proton ceramic fuel cells with low polarization losses by optimizing the composition of the inlet hydrogen fuel.