We present a survey of interstellar Zn II and Cr II absorption extracted from the Hubble Space Telescope Goddard High Resolution Spectrograph (HST GHRS) data archive. We find clear evidence for an enhanced depletion of Zn from the gas phase with increasing fractional abundance of molecular hydrogen f(H2). Our lower limit to the Galactic interstellar metallicity is approximately 65% of the solar value as determined by the measured Zn abundances in the lowest f(H2) sightlines, (N(Zn)/N(H(sup 0)(sub tot)) = -0.19 +/- 0.04. The correspondingly high depletion of Cr with respect to solar (N(Cr/N(H(sup 0)(sub tot)) = -1.44 +/- 0.26 indicates that there are significant amounts of dust present in these lines of sight. The Galactic abundances of Zn and Cr in the ISM provide a fundamental reference point which is used to understand the metal enrichment and dust formation history of damped Lyman alpha QSO absorption-line systems, normally believed to arise from intervening precursors to modern disk galaxies. Although the spread in Zn abundances is large for both the local ISM and in damped Lyman alpha systems, we still find a substantial difference (factor of 4-10) in metallicity between the two sets. This survey and future observations of more distant objects which probe the full extent of the Milky Way halo provide a more complete picture of the enrichment and depletion characteristics of present-day galaxies.