We present echelle-resolution (FWHM approximately 5 km s-1) HST observations of Mg II, Mg I, and ground-based observations of Na I absorption toward SN 1993J which exploded in M81. We detect individual absorption components spanning a total velocity range of -163 < upsilon. < + 225 km s-1. The components are grouped into three subcomplexes, representing absorption from the disk of M81, from our own Galactic disk and halo, and from intergalactic gas which is probably the tidal debris of interactions between M81 and M82. We use the Mg I/Na I ratios to estimate the temperature of the absorbing gas; many of the components have high ratios, indicative of T > 7000 K, and so originate in the warm, diffuse ionized medium of our own Galaxy, of M81, and of the disrupted ps.