We examined liquidus phase relations in Fe-O+/-H at ~40 and ~150 GPa, and subsolidus phase equilibria in Fe-FeH. While it has been speculated that Fe and FeH form continuous solid solution to core pressures, our experiments show the coexistence of the H-poor hcp and H-rich fcc phases in the Fe-FeH system. Considering higher melting temperature of stoichiometric FeH than that of Fe-FeH, it indicates eutectic melting between Fe and FeH. It is consistent with the liquidus phase diagram in Fe-O-H, which implies the Fe-FeH binary eutectic liquid composition of FeH0.42 at ~40 GPa. We estimated the outer core liquid composition to be Fe + 2.9-5.2% O + 0.03-0.32% H + 0-3.4% Si + 1.7% S by weight, based on the liquidus phase relations, solid-liquid partitioning, and outer/inner core densities and velocities, indicating that O and either H or Si are important core light elements.