ZnO films co-doped with fluorine and hydrogen were prepared on Corning glass by radio frequency magnetron sputtering of ZnO targets with varying amounts of ZnF2 in H2/Ar gas mixtures of varying H2 content. The ZnO films' electrical, optical, and structural properties in combination with their compositional properties were investigated. A small addition of H2 to the sputtering gas caused a drastic increase of Hall mobility with a marginal increase in carrier concentration, indicating an effective passivation of grain boundaries due to hydrogenation. For further increase of H2 in sputter gas, the Hall mobility remained at a relatively constant level while the carrier concentration increased steadily. Most of the ZnO films co-doped with fluorine and hydrogen showed average transmittance higher than 83% in the 400-800 nm range, while the average absorption coefficients were lower than 600 cm(-1), implying very low absorption loss in these films. It was discovered that the fabrication of ZnO films with a Hall mobility higher than 40 cm2/Vs and a very low absorption loss in the visible range is possible by co-doping hydrogen and fluorine.