The ternary mixture of uranium, zirconium and oxygen is investigated as a minimal model for corium, the mixture that forms after the meltdown of a nuclear reactor. Like corium, U-Zr-O exhibits a liquid-liquid phase separation between a metal-rich and an oxyde-rich phase at high temperatures. A CALPHAD database built on an associate model is used to set up a ternary Cahn-Hilliard model, which can describe two-phase patterns in U-Zr-O and may be coupled to the Navier-Stokes equations for hydrodynamic flows. The interface structure and properties, which depend on the choice on the gradient energy coefficients in the free-energy functional, are studied in detail. It is found that interface adsorption is generally present, but that its magnitude is small, such that the model remains a robust and useful tool for future simulations of corium pool stratification dynamics.