  We characterize the column density probability distributions functions (PDFs)
of the atomic hydrogen gas, HI, associated with seven Galactic molecular clouds
(MCs). We use 21 cm observations from the Leiden/Argentine/Bonn Galactic HI
Survey to derive column density maps and PDFs. We find that the peaks of the HI
PDFs occur at column densities ranging from ~1-2$\times 10^{21}$ cm$^2$
(equivalently, ~0.5-1 mag). The PDFs are uniformly narrow, with a mean
dispersion of $\sigma_{HI}\approx 10^{20}$ cm$^2$ (~0.1 mag). We also
investigate the HI-to-H$_2$ transition towards the cloud complexes and estimate
HI surface densities ranging from 7-16 $M_\odot$ pc$^{-2}$ at the transition.
We propose that the HI PDF is a fitting tool for identifying the HI-to-H$_2$
transition column in Galactic MCs.
