Ultraviolet spectra (912-3300 Angstrom) from the Astro-1 and IUE space missions of two Herbig Be stars, HD 45677 and HD 200775, show that the HD 200775 intrinsic continuum shape generally coincides with a T = 20,000 K Kurucz model and that the HD 45677 continuum exhibits additional line blanketing; extinction, and emission from gas and dust in its disk and bipolar wind. With log N(H I)= 21.4 +/- 0.1 cm(-1), our measured upper limit on the fraction of HD 45677 disk H atoms in molecules (f < 1.5 x 10(-2)) is much less than that seen in general Galactic molecular clouds (f approximate to 0.5). Also, our derived HD 45677 circumstellar dust extinction for lambda > 1400 Angstrom is produced by an inhomogeneous disk of material: during periods of moderate visual extinction (A(v) approximate to 1.0 +/- 0.3 mag) the disk as a whole causes mid-UV extinction with an R(v) x 4-5 (values found in Galactic molecular clouds), yet at the thickest optical depths, there are regions with larger grains (inferred R(v) > 7) than those in molecular clouds (R(v) < 5.6). Alternately, we find in the FUV (1300-1000 Angstrom) a strong, steeply curved circumstellar extinction for HD 45677 that has a very similar shape as extinction produced by interstellar polycyclic aromatic hydrocarbon molecules (PAHs) in an illuminated molecular cloud (NGC 2023). The PAHs around HD 45677, like NGC 2023, are more abundant relative to the large grains (A lambda A(v)) than predicted by the extinction parameter R(v) because HD 45677 has evaporated the PAHs off large grains. With a measured FUV depth corresponding to tau(lambda) approximate to 1.4-3.5, the excess PAHs around HD 45677 partly shield the outer disk from FUV radiation. Both the disk gas and dust have evolved greatly since the formation of the midmass star HD 45677 from molecular clouds: in some regions, the disk grains have grown to micron sizes suitable for the formation of planetesimals, the ISM H-2 has been photodissociated into H I in the disk, and CO (McGregor, Hyland, and Hillier 1988) has disappeared. In addition, the molecular PAHs that are condensed onto grains in molecular clouds have photoevaporated off grains into the gaseous disk of HD 45677, becoming dehydrogenated and ionized. Thus, because of strong FUV radiation from HD 45677 and moderate FUV shielding, the disk around this intermediate-mass star differs dramatically from the condensate-rich, molecular gas around low-mass stars and would seem to lead to a different chemical and physical evolution toward planets than those around low-mass stars such as our Sun.