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We discuss the absorption due to various constituents of the interstellar medium (ISM) of M82 seen in moderately high-resolution, high signal-to-noise ratio optical spectra of SN 2014J. Complex absorption from M82 is seen, at velocities 45 ≲ v_LSR ≲ 260 km/s, for Na I, K I, Ca I, Ca II, CH, CH⁺, and CN; many of the diffuse interstellar bands (DIBs) are also detected. Comparisons of the column densities of the atomic and molecular species and the equivalent widths of the DIBs reveal both similarities and differences in relative abundances, compared to trends seen in the ISM of our Galaxy and the Magellanic Clouds. Of the 10 relatively strong DIBs considered here, 6 (including λ5780.5) have strengths within ±20% of the mean values seen in the local Galactic ISM, for comparable N(K I); 2 are weaker by 20%-45% and 2 (including λ5797.1) are stronger by 25%-40%. Weaker than "expected" DIBs (relative to N(K I), N(Na I), and E(B - V)) in some Galactic sight lines and toward several other extragalactic supernovae appear to be associated with strong CN absorption and/or significant molecular fractions. While the N(CH)/N(K I) and N(CN)/N(CH) ratios seen toward SN 2014J are similar to those found in the local Galactic ISM, the combination of high N(CH⁺)/N(CH) and high W(5797.1)/W(5780.5) ratios has not been seen elsewhere. The centroids of many of the M82 DIBs are shifted relative to the envelope of the K I profile–likely due to component-to-component variations in W(DIB)/N(K I) that may reflect the molecular content of the individual components. We compare estimates for the host galaxy reddening E(B - V) and visual extinction A_V derived from the various interstellar species with the values estimated from optical and near-IR photometry of SN 2014J.