In this work, p-type oxide semiconductors, Co3O4 and complex oxides NixCo3−xO4 (x = 0.04, 0.07, 0.1), were studied as materials for sub-ppm H2S sensing in the temperature range of 90–300 °C in dry and humid air. Nanocrystalline Co3O4 and NixCo3−xO4 (x = 0.04, 0.07, 0.1) were prepared by coprecipitation of cobalt and nickel oxalates from nitrate solutions and further annealing at 300 °C. The surface reactivity of the obtained materials toward H2S both in dry and humid atmosphere (relative humidity at 25 °C R.H. = 60%) was investigated using diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS). Sensor measurements showed a decrease in sensor signal toward 1 ppm H2S with an increase in Ni content because of a decrease in chemisorbed surface oxygen species. On the other hand, sensor signal increases for all samples with increasing the relative humidity that depends on reactivity of the surface hydroxyl groups, which stimulate the decomposition of surface sulfites and provide better surface regeneration at higher temperature. This assumption was additionally confirmed by the faster saturation of the conductivity curve and a decrease in the sensor response time in humid air.