High-dispersion (25 km s-1 FWHM) spectra from the International Ultraviolet Explorer (IUE) satellite were analyzed in order to obtain information about the density distribution of interstellar Al III away from the galactic plane. From the data for a group of 70 stars including SN 1987A, we were able to measure equivalent widths of the interstellar Al III lines at λλ1854.720 and 1862.795 for sight lines toward 29 galactic stars and toward two extragalactic objects. Problems with stellar blending of photospheric Al III with the interstellar lines resulted in the rejection of the data for most of the remaining 40 stars. The measurements were from single or multiple spectra obtained from the data of various surveys of Milky Way halo gas and from the IUE archives. The Al III lines are situated in a high-sensitivity region of the IUE detector, and the data generally have higher signal-to-noise ratio than for the important lines of C IV, Si IV, and N V found at shorter wavelengths. In most cases the measured values of the Al III relative line strengths are consistent with only modest levels of line saturation. The equivalent widths were converted to estimates of log N (atoms cm-2) and the doppler spread parameter, b (km s-1). Al III is created by ionizing radiation with E > 18.82 eV and is destroyed by radiation having E > 28.44 eV. The program stars were generally selected to avoid regions of obvious photoionized nebulosity in order to study the general galactic distribution of Al III. Measures of N(H I) are available for all the program stars through measures of the H I Lyα line. The distributions of Al III and H I away from the galactic plane are studied by examining plots of log Nx|sin b|versus log |z| where b is the star's latitude and |z| is its distance away from the galactic plane. From those plots we find that Al III has an exponential scale height and 1 σ errors of 1.02(+0.36, -0.24) kpc. For the same set of stars, the scale height and 1 σ errors for H I are 0.67(+0.21, -0.16) kpc. The Al III scale height is similar to the value of 0.89(+0.25, -0.18) kpc obtained for free electrons from pulsar dispersion measures. The ionized gas traced by Al III is somewhat more extended than the neutral gas traced by H I, but less extended than the very highly ionized gas traced by Si IV, C IV, and N V which has a scale height estimated by Savage and Massa (1987) to be 2 to 3 kpc.