We use the COBE(8) Differential Microwave Radiometers (DMR) 4 yr sky m
aps to model Galactic microwave emission at high latitudes (\b\ > 20 d
egrees). Cross-correlation of the DMR maps with Galactic template maps
detects fluctuations in the high-latitude microwave sky brightness wi
th the angular variation of the DIRBE far-infrared dust maps and a fre
quency dependence consistent with a superposition of dust and free-fre
e emission. We find no significant correlations between the DMR maps a
nd various synchrotron templates. On the largest angular scales (e.g.,
quadrupole), Galactic emission is comparable in amplitude to the anis
otropy in the cosmic microwave background (CMB). The CMB quadrupole am
plitude, after correction for Galactic emission, has amplitude Q(rms)
= 10.7 mu K with random uncertainty 3.6 mu K and systematic uncertaint
y 7.1 mu K from uncertainty in our knowledge of Galactic microwave emi
ssion.