The separation of immiscible liquids has significant implications for magma evolution and the formation of magmatic ore deposits. We combine high-resolution imaging and electron probe microanalysis with the first use of atom probe tomography on tholeiitic basaltic glass from Hawaii, the Snake River Plain, and Iceland, to investigate the onset of unmixing of basaltic liquids into Fe-rich and Si-rich conjugates. We examine the relationships between unmixing and crystal growth, and the evolution of a nanoemulsion in a crystal mush. We identify the previously unrecognised role played by compositional boundary layers in promoting unmixing around growing crystals at melt-crystal interfaces. Our findings have important implications for the formation of immiscible liquid in a crystal mush, the interpretations of compositional zoning in crystals, and the role of liquid immiscibility in controlling magma physical properties.