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 similar to 3.8 GPa and hydrogen solidified at similar to 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.