Injection at pressures exceeding the propellant critical pressures is typically considered a diffuse interface mixing process rather than a sharp interface break-up. However, this is not necessarily the case in mixtures where the local mixture critical pressure may exceed the value of the pure components. So far, there is no canonical theoretical or computational model to analyze local phase separation under these conditions. In the present paper, we propose to separate the problem into two aspects: determination of local mixture temperature and composition, and analysis of the local thermochemical state. We calculate transport of mass, momentum, energy, and species using a large-eddy simulation (LES) method to obtain an accurate local state. This local state is then assessed via a vapor-liquid equilibrium solution using the Peng-Robinson equation of state. We apply this methodology to three technically relevant mixing problems at propellant supercritical pressures: inert nitrogen/n-dodecane injection, an inert liquid oxygen/gaseous hydrogen shear layer, and a reacting liquid oxygen/gaseous hydrogen shear layer. The last case represents the first phase analysis of a reacting case; we show that it can be reduced to the binary mixing of oxygen and water. Counterintuitively, the reacting LOX/GH2 shear layer is more susceptible to phase separation than the inert mixing case, despite the high temperatures reached in the flame. Finally, we compare the mixture critical loci obtained from the canonical computational fluid dynamics mixing rules with results obtained from vapor liquid equilibrium calculations, and show that both are fundamentally, qualitatively different.