Much of the interstellar medium in disk galaxies is in the form of neutral atomic hydrogen, H i. This gas can be in thermal equilibrium at relatively low temperatures, Td300 K (the cold neutral medium (CNM)), or at temperatures somewhat less than 10 4 K (the warm neutral medium (WNM)). These two phases can coexist over a narrow range of pressures, PminPPmax. We determine Pmin and Pmax in the plane of the Galaxy as a function of Galactocentric radius R using recent determinations of the gas heating rate and the gas-phase abundances of interstellar gas. We provide an analytic approximation for Pmin as a function of metallicity, far-ultraviolet radiation field, and the ionization rate of atomic hydrogen. Our analytic results show that the existence of Pmin, or the possibility of a two-phase equilibrium, generally requires that H + exceed C + in abundance at Pmin. The abundance of H + is set by EUV/soft X-ray photoionization and by recombination with negatively charged polycyclic aromatic hydrocarbons. In order to assess whether thermal or pressure equilibrium is a realistic assumption, we define a parameter � � tcool=tshock, where tcool is the gas cooling time and tshock is the characteristic shock time or '' time between shocks in a turbulent medium.'' For � < 1 gas has time to reach thermal balance between supernova-induced shocks. We find that this condition is satisfied in the Galactic disk, and thus the two-phase description of the interstellar H i is approximately valid even in the presence of interstellar turbulence. Observationally, the mean density nHi hi is often better determined than the local density, and we cast our results in terms of nHi hi as well. Over most of the disk of the Galaxy, the Hi must be in two phases: the weight of the Hi in the gravitational potential of the Galaxy is large enough to generate thermal pressures exceeding Pmin, so that turbulent pressure fluctuations can produce cold gas that is thermally stable; and the mean density of the H i is too low for the gas to be all CNM. Our models predict the presence of CNM gas to R ' 16 18 kpc, somewhat farther than previous estimates. An estimate for the typical thermal pressure in the Galactic plane for 3 kpcdRd18 kpc is Pth=k ' 1:4 � 10 4 expð� R=5:5 kpcÞ Kc m � 3 . At the solar circle, this gives Pth=k ' 3000 K cm � 3 . We show that this pressure is consistent with the C i*/C itot ratio observed by Jenkins & Tripp and the CNM temperature found by Heiles & Troland. We also examine the potential impact of turbulent heating on our results and provide parameterized expressions for the heating rate as a function of Galactic radius. Although the uncertainties are large, our models predict that including turbulent heating does not significantly change our results and that thermal pressures remain above Pmin to R ' 18 kpc. Subject headings: ISM: clouds — ISM: general — ISM: structure