  We combine Herschel observations of a total of 12 sources to construct the
most uniform survey of HF and H2O in our Galactic disk. Both molecules are
detected in absorption along all sight lines. The high spectral resolution of
the Heterodyne Instrument for the Far-Infrared (HIFI) allows us to compare the
HF and H2O distributions in 47 diffuse cloud components sampling the disk. We
find that the HF and H2O velocity distributions follow each other almost
perfectly and establish that HF and H2O probe the same gas-phase volume. Our
observations corroborate theoretical predictions that HF is a sensitive tracer
of H2 in diffuse clouds, down to molecular fractions of only a few percent.
Using HF to trace H2 in our sample, we find that the N(H2O)-to-N(HF) ratio
shows a narrow distribution with a median value of 1.51. Our results further
suggest that H2O might be used as a tracer of H2 -within a factor 2.5- in the
diffuse interstellar medium. We show that the measured factor of ~2.5 variation
around the median is driven by true local variations in the H2O abundance
relative to H2 throughout the disk. The latter variability allows us to test
our theoretical understanding of the chemistry of oxygen-bearing molecules in
the diffuse gas. We show that both gas-phase and grain-surface chemistry are
required to reproduce our H2O observations. This survey thus confirms that
grain surface reactions can play a significant role in the chemistry occurring
in the diffuse interstellar medium n_H < 1000 cm^-3.
