We present an analysis of interstellar neutral hydrogen column densities obtained from archival Lyalpha absorption line data toward the complete sample of B2 and hotter stars observed at high spectral resolution with the IUE satellite. The full sample includes 554 stars and more than doubles the number of lines of sight previously observed. Many of the B2 and BI.5 stars exhibit contamination from stellar Lyalpha absorption, and were excluded from the subsequent analysis. The final working sample includes 393 stars. We present statistical averages for a number of quantities derived for the sample. The stars range in distance from 0.12 to 11 kpc with an average distance of 2.1 kpc. Values for average sight-line density range from 0.017 to 8.62 atoms cm-3, with an overall average of 0.23 atoms cm-3. Neutral hydrogen and dust are well correlated, with [N(H I)/E(B-V)] = 4.93 x 10(21) cm-2 mag-1, and [N(H I)/E(Bump)] = 2.17 x 10(21) cm-2 mag-1. There is an increase in the H i to dust ratios for the densest sight lines. Evidently, the H I to dust ratios in dense clouds are higher than in the lower density medium between the clouds and in interarm directions. The effect is probably an indication of dust modification in the dense clouds. The H I to dust ratios are approximately 17% smaller for the sight lines to 0 stars compared to the ratios found toward B stars. We have identified sight lines with anomalously large and small values of N(H I)/E(B-V) and N(H I)/E(Bump). Some of these sight lines are well-known examples of peculiar extinction (i.e., HD 147933 and HD 37061 [NU Ori]). Others are less well known and may provide important new examples of regions with highly modified dust. The number of stars with anomalously low H I to dust ratios is disproportionately larger than the number of stars with anomalously high H I to dust ratios. The distribution of the gas away from the Galactic plane for the sample of objects is complex. For the subset of 375 stars whose lines of sight have a statistically low probability of intersecting a large cloud, the distribution may be roughly approximated by an exponential density distribution, with a midplane density of 0.366 atoms cm-3, a scale height of 195 pc, and a random logarithmic scattering parameter sigma(p) of 0.159 dex. For the same sample of stars, interstellar dust is found to be confined closer to the plane than the H I, with [E(B-V)/r]0 = 0.257 mag kpc-1, scale height h = 152 pc, and sigma(p) = 0.263 dex. The dust distribution is more inhomogeneous than the gas distribution. The observed distribution of H I away from the Galactic plane can also be fitted with a two-component exponential model including the effects of patchiness. Unfortunately, the foreground contamination produced by the cloudy and more confined component of H I makes it difficult to estimate the scale height of the extended component without invoking an independent estimate of its midplane density. Assuming n2(0) = 0.16 cm-3 from the Copernicus satellite H I/H-2 survey, we obtain n1(0) = 0.247 cm-3, h1 = 73 pc, and h2 + 357 pc.
