A new study of the diffuse Galactic gamma-ray continuum radiation is presen
ted, using a cosmic-ray propagation model which includes nucleons, antiprot
ons, electrons, positrons, and synchrotron radiation. Our treatment of the
inverse Compton scattering includes the effect of anisotropic scattering in
the Galactic interstellar radiation held (ISRF) and a new evaluation of th
e ISRF itself. Models based on locally measured electron and nucleon spectr
a and synchrotron constraints are consistent with gamma-ray measurements in
the 30-500 MeV range, but outside this range excesses are apparent. A hard
er nucleon spectrum is considered but fitting to gamma-rays causes it to vi
olate limits from positrons and antiprotons. A harder interstellar electron
spectrum allows the gamma-ray spectrum to be fitted above 1 GeV as well, a
nd this can be further improved when combined with a modified nucleon spect
rum which still respects the limits imposed by antiprotons and positrons. A
large electron/inverse Compton halo is proposed which reproduces well the
high-latitude variation of gamma-ray emission; this is taken as support for
the halo size for nucleons deduced from studies of cosmic-ray composition.
Halo sizes in the range 4-10 kpc are favored by both analyses. The halo co
ntribution of Galactic emission to the high-latitude gamma-ray intensity is
large, with implications for the study of the diffuse extragalactic compon
ent and signatures of dark matter. The constraints provided by the radio sy
nchrotron spectral index do not allow all of the gamma-ray emission at less
than 30 MeV to be explained in terms of a steep electron spectrum unless t
his takes the form of a sharp upturn below 200 MeV. This leads us to prefer
a source population as the origin of the excess low-energy gamma-rays, whi
ch can then be seen as a continuation of the hard X-ray continuum measured
by OSSE, Ginga, and RXTE.