Liquid-liquid interfaces and nucleation in partially miscible Lennard-Jones (LJ) mixtures are considered using density functional theory. We present phase diagrams, interfacial liquid-vapor and liquid-liquid profiles, and gas-liquid as well as liquid-liquid surface tensions for two types of mixtures having different mixing rules for the LJ energy parameter. A simple local density approximation does not give oscillatory behavior at the liquid-liquid interface, but a more realistic weighted density approximation does show this behavior. Both approaches also give a total density minimum near the interface, comparable to that found in molecular dynamics and integral equation studies. Finally, we calculate the density profiles and free energies for critical nuclei in liquid-liquid phase separation.