We use absolutely calibrated data from the ARCADE 2 flight in July 2006 to model Galactic emission at frequencies 3, 8, and 10 GHz. The spatial structure in the data is consistent with a superposition of free-free and synchrotron emission. Emission with spatial morphology traced by the Haslam 408 MHz survey has spectral index beta_synch = -2.5 +/- 0.1, with free-free emission contributing 0.10 +/- 0.01 of the total Galactic plane emission in the lowest ARCADE 2 band at 3.15 GHz. We estimate the total Galactic emission toward the polar caps using either a simple plane-parallel model with csc|b| dependence or a model of high-latitude radio emission traced by the COBE/FIRAS map of CII emission. Both methods are consistent with a single power-law over the frequency range 22 MHz to 10 GHz, with total Galactic emission towards the north polar cap T_Gal = 0.498 +/- 0.028 K and spectral index beta = -2.55 +/- 0.03 at reference frequency 1 GHz. The well calibrated ARCADE 2 maps provide a new test for spinning dust emission, based on the integrated intensity of emission from the Galactic plane instead of cross-correlations with the thermal dust spatial morphology. The Galactic plane intensity measured by ARCADE 2 is fainter than predicted by models without spinning dust, and is consistent with spinning dust contributing 0.4 +/- 0.1 of the Galactic plane emission at 22 GHz.