Binary mixtures of hydrogen and ammonia were compressed in diamond anvil cells to 15 GPa at room temperature over a range of compositions. The phase behavior was characterized using optical microscopy, Raman spectroscopy, and synchrotron X-ray diffraction. Below 1.2 GPa we observed two-phase coexistence between liquid ammonia and fluid hydrogen phases with limited solubility of hydrogen within the ammonia-rich phase. Complete immiscibility was observed subsequent to the freezing of ammonia phase III at 1.2 GPa, although hydrogen may become metastably trapped within the disordered face-centered-cubic lattice upon rapid solidification. For all compositions studied, the phase III to phase IV transition of ammonia occurred at ~3.8 GPa and hydrogen solidified at ~5.5 GPa, transition pressures equivalent to those observed for the pure components. A P-x phase diagram for the NH(3)-H(2) system is proposed on the basis of these observations with implications for planetary ices, molecular compound formation, and possible hydrogen storage materials.