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 $N_H = (7.4pm0.1)times 10^{21}$ 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 $N_H = 4.4times 10^{21}$ 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$=$$16pm10$ eV) and narrow (FWMH$<$5,500 km s$^{-1}$, consistent with optical H$alpha$) Fe K$alpha$ emission line at E$=$6.4 keV likely from the torus in the central regions of 3C 111, and we place an upper limit on the column density of a possible intrinsic warm absorber of $N_H$$<$$2.5times10^{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.
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