Using the echelle-A grating of the Goddard High-Resolution Spectrograph, we have observed the C II λλ1335, 1336 emission lines of the nearby (d = 13.3 pc) star system Capella (G8 III + G1 III). Interstellar C II absorption features are detected within both stellar emission lines. The ground-state and excited-state C II column densities derived from these absorption lines imply an electron density of ne = 0.11+0.12-0.06 cm-3 in the local interstellar medium (LISM). Unlike previous derivations of ne from Mg II/Mg I ratios, the density suggested by the C II lines is independent of assumptions about ionization equilibrium. Current estimates of the H I density in the LISM are in the range 0.1-0.2 cm-3. The He I/H I ratio toward the white dwarf G191-B2B, which is only 7° from Capella, has been measured to be He I/H I = 0.068-0.082 from the Extreme-Ultraviolet Explorer data. These results indicate hydrogen and helium ionization fractions toward Capella of X(H) = 0.45 +/- 0.25 and X(He) = 0.57 +/- 0.23, respectively, confirming that hydrogen and helium are substantially ionized in the LISM.Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy Inc., under NASA contract NAS5-26555.