  We show the combined spectral analysis of \emph{Chandra} high energy
transmission grating (HETG) and \emph{XMM-Newton} reflection grating
spectrometer (RGS) observations of the broad-line radio galaxy 3C 111. The
source is known to show excess neutral absorption with respect to the one
estimated from 21 cm radio surveys of atomic H I in the Galaxy. However,
previous works were not able to constrain the origin of such absorber as local
to our Milky Way or intrinsic to the source ($z = 0.0485$). The high
signal-to-noise grating spectra allow us to constrain the excess absorption as
due to intervening gas in the Milky Way, and we estimate a time averaged total
column density of $N_H = (7.4\pm0.1)\times 10^{21}$ cm$^{-2}$, a factor of two
higher than the tabulated H I value. We recommend to use the total average
Galactic column density here estimated when studying 3C 111. The origin of the
extra Galactic absorption of $N_H = 4.4\times 10^{21}$ cm$^{-2}$ is likely due
to molecular gas associated with the Taurus molecular cloud complex toward 3C
111, which is our nearest star-forming region. We also detect a weak
(EW$=$$16\pm10$ eV) and narrow (FWMH$<$5,500 km s$^{-1}$, consistent with
optical H$\alpha$) Fe K$\alpha$ emission line at E$=$6.4 keV likely from the
torus in the central regions of 3C 111, and we place an upper limit on the
column density of a possible intrinsic warm absorber of
$N_H$$<$$2.5\times10^{20}$ cm$^{-2}$. These complexities make 3C 111 a very
promising object for studying both the intrinsic properties of this active
radio galaxy and the Galactic interstellar medium if used as a background
source.
