The recent Hubble Space Telescope (HST) observations of the z(q) = 3.286 quasar Q0302-003 (Jakobeen et al. 1994) and the z(q) = 3.185 quasar Q1935-67 by Tytler (1995) show absorption edges at the redshifted wavelength of He II 304 Angstrom. A key goal is to distinguish between contributions from discrete Ly alpha forest clouds and a smoothly distributed intergalactic medium (IGM). We model the contributions from each of these sources of He II absorption, including the distribution of line Doppler widths and column densities, the ''He II proximity effect'' from the quasar, and a self-consistent derivation of the He Il opacity of the universe as a function of the spectrum of ionizing sources, with the assumption that both the clouds and the IGM are photoionized. The He II edge can be fully accounted for by He II line blanketing for reasonable distributions of line widths and column densities in the Ly alpha forest, provided that the ionizing sources have spectral index alpha(s) > 1.5, and any He II proximity effect is neglected. Even with some contribution from a diffuse IGM, it is difficult to account for the edge observed by Jakobsen et al. (1994) with a ''hard'' source spectrum (alpha(s), < 1.3). The proximity effect modifies the relative contributions of the clouds and IGM to tau(HeII), near the quasar (z less than or similar to z(q)) and markedly increases the amount of He II absorption required. This implies, for example, that to account for the He II edge with line blanketing alone, the minimum spectral index a(s) must be increased from 1.5 to 1.9. We demonstrate the need for higher resolution observations that characterize the change in transmission as z --> z(q) and resolve line-free gaps in the continuum. We set limits on the density of the diffuse IGM and suggest that the IGM and Ly alpha clouds are likely to be a significant repository for dark baryons.