  We report Arecibo 21 cm absorption-emission observations to characterise the
physical properties of neutral hydrogen (HI) in the proximity of five giant
molecular clouds (GMCs): Taurus, California, Rosette, Mon OB1, and NGC 2264.
Strong HI absorption was detected toward all 79 background continuum sources in
the ~60x20 square degree region. Gaussian decompositions were performed to
estimate temperatures, optical depths and column densities of the cold and warm
neutral medium (CNM, WNM). The properties of individual CNM components are
similar to those previously observed along random Galactic sightlines and in
the vicinity of GMCs, suggesting a universality of cold HI properties. The CNM
spin temperature (Ts) histogram peaks at ~50K. The turbulent Mach numbers of
CNM vary widely, with a typical value of ~4, indicating that their motions are
supersonic. About 60% of the total HI gas is WNM, and nearly 40% of the WNM
lies in thermally unstable regime 500-5000K. The observed CNM fraction is
higher around GMCs than in diffuse regions, and increases with increasing
column density (NHI) to a maximum of ~75%. On average, the optically thin
approximation (N*(HI)) underestimates the total N(HI) by ~21%, but we find
large regional differences in the relationship between N(HI) and the required
correction factor, f=N(HI)/N*(HI). We examine two different methods (linear fit
of f vs log10(N*(HI)) and uniform Ts) to correct for opacity effects using
emission data from the GALFA-HI survey. We prefer the uniform Ts method, since
the linear relationship does not produce convincing fits for all subregions.
