We unravel the complex chemistry in both the neutral and ionic systems of a radio-frequency-driven atmospheric-pressure plasma in a helium-oxygen mixture (He-0.5% O) with air impurity levels from 0 to 500 ppm of relative humidity from 0% to 100% using a zero-dimensional, time-dependent global model. Effects of humid air impurity on absolute densities and the dominant production and destruction pathways of biologically relevant reactive neutral species are clarified. A few hundred ppm of air impurity crucially changes the plasma from a simple oxygen-dependent plasma to a complex oxygen-nitrogen-hydrogen plasma. The density of reactive oxygen species decreases from 10 to 10 cm, which in turn results in a decrease in the overall chemical reactivity. Reactive nitrogen species (10 cm ), atomic hydrogen and hydroxyl radicals (10-10 cm) are generated in the plasma. With 500 ppm of humid air impurity, the densities of positively charged ions and negatively charged ions slightly increase and the electron density slightly decreases (to the order of 10 cm). The electronegativity increases up to 2.3 compared with 1.5 without air admixture. Atomic hydrogen, hydroxyl radicals and oxygen ions significantly contribute to the production and destruction of reactive oxygen and reactive nitrogen species.