  (Abridged) Using the Arecibo Observatory we have obtained neutral hydrogen
(HI) absorption and emission spectral pairs in the direction of 26 background
radio continuum sources in the vicinity of the Perseus molecular cloud. Strong
absorption lines were detected in all cases allowing us to estimate spin
temperature (T_s) and optical depth for 107 individual Gaussian components
along these lines of sight. Basic properties of individual HI clouds (spin
temperature, optical depth, and the column density of the cold and warm neutral
medium, CNM and WNM) in and around Perseus are very similar to those found for
random interstellar lines of sight sampled by the Millennium HI survey. This
suggests that the neutral gas found in and around molecular clouds is not
atypical. However, lines of sight in the vicinity of Perseus have on average a
higher total HI column density and the CNM fraction, suggesting an enhanced
amount of cold HI relative to an average interstellar field. Our estimated
optical depth and spin temperature are in stark contrast with the recent
attempt at using Planck data to estimate properties of the optically thick HI.
Only ~15% of lines of sight in our study have a column density weighted average
spin temperature lower than 50 K, in comparison with >85% of Planck's sky
coverage. The observed CNM fraction is inversely proportional to the
optical-depth weighted average spin temperature, in excellent agreement with
the recent numerical simulations by Kim et al. While the CNM fraction is on
average higher around Perseus relative to a random interstellar field, it is
generally low, 10-50%. This suggests that extended WNM envelopes around
molecular clouds, and/or significant mixing of CNM and WNM throughout molecular
clouds, are present and should be considered in the models of molecule and star
formation.
