Cold atmospheric pressure plasma jets (CAPJs) are an emerging technology for the localised treatment of heat sensitive surfaces. Adding humidity to the CAPJ’s feed gas yields an effective production of highly reactive intermediate species, such as hydrogen atoms, oxygen atoms, and hydroxyl radicals, among others, which are key species for biomedical applications. This study focusses on the effluent of the CAPJ kINPen, which was operated with argon feed gas and a humidity admixture of 3000 ppm, while a gas curtain was used to limit the diffusion of ambient air into the effluent. The axial and radial density distribution of O and H atoms is measured by means of picosecond two-photon absorption laser induced fluorescence spectroscopy (ps-TALIF). A maximum O atom density of (3.8 ± 0.7) × 1015 cm−3 and a maximum H atom density of (3.5 ± 0.7) × 1015 cm−3 are found at the nozzle of the plasma jet. The experimental results are compared to a two-dimensional reacting flow model that is coupled with a local zero-dimensional plasma chemical model. With this model, the main H and O atom production mechanisms are determined to be the dissociation of H2O and O2 in the plasma zone of the plasma jet. The latter indicates, that a significant amount of oxygen (1%) was present inside the device. The reaction of OH with O atoms represents the main consumption pathway for O atoms and is at the same time a significant production pathway for H atoms. The main consumption of H atoms is through a three-body reaction including O2 to form HO2, which consumes more H and O atoms to form OH. It is pointed out, that most of the species are produced in the plasma zone, and that O and H atoms, OH and HO2 radicals, and O2 and H2O molecules are strongly connected.