We describe the interface between the outer heliosphere and the local interstellar medium (LISM) surrounding the Sun. The components of the inner LISM are the four partially ionized clouds [the Local Interstellar Cloud (LIC), G cloud, Blue cloud, andAql cloud] that are in contact with the outer heliosphere, and ionized gas produced by EUV radiation primarily from ǫ CMa. We construct the three-dimensional shape of the LIC based on interstellar line absorption along 62 sightlines and show that in the direction of ǫ CMa, β CMa, and Sirius B the neutral hydrogen column density from the center of the LIC is a minimum. We call this region the "hydrogen hole". In this direction, the presence of Blue cloud absorption and the absence of LIC absorption can be simply explained by the Blue cloud lying just outside of the heliosphere. We propose that the outer edge of the Blue cloud is a Strömgren shell driven toward the heliosphere Corresponding author: Jeffrey L. Linsky jlinsky@jila.colorado.edu * Based on observations made with the NASA/ESA Hubble Space Telescope obtained from the Data Archive at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS AR-09525.01A. These observations are associated with programs #12475, 12596.Linsky, Redfield, and Tilipman by high pressures in the H II region. We find that the vectors of neutral and ionized helium flowing through the heliosphere are inconsistent with the LIC flow vector, and that the nearby intercloud gas is consistent with ionization by ǫ CMa and other stellar sources without requiring additional sources of ionization or million degree plasma. In the upwind direction, the heliosphere is passing through an environment of several LISM clouds, which may explain the recent influx of interstellar grains containing 60 Fe from supernova ejecta measured in Antarctica snow.