We present the results from a joint Suzaku/NuSTAR broad-band spectral analysis of 3C 390.3. The high quality data enables us to clearly separate the primary continuum from the reprocessed components allowing us to detect a high energy spectral cut-off ($E_\text{cut}=117_{-14}^{+18}$ keV), and to place constraints on the Comptonization parameters of the primary continuum for the first time. The hard over soft compactness is 69$_{-24}^{+124}$ and the optical depth 4.1$_{-3.6}^{+0.5}$, this leads to an electron temperature of $30_{-8}^{+32}$ keV. Expanding our study of the Comptonization spectrum to the optical/UV by studying the simultaneous Swift-UVOT data, we find indications that the compactness of the corona allows only a small fraction of the total UV/optical flux to be Comptonized. Our analysis of the reprocessed emission show that 3C 390.3 only has a small amount of reflection (R~0.3), and of that the vast majority is from distant neutral matter. However we also discover a soft X-ray excess in the source, which can be described by a weak ionized reflection component from the inner parts of the accretion disk. In addition to the backscattered emission, we also detect the highly ionized iron emission lines Fe XXV and Fe XXVI.