Rock-ice avalanches are rapid, catastrophic mass flows consisting of massive rock and ice particles in alpine regions. Varying material properties of rock and ice particles cause them to spontaneously mix and segregate during the flow. However, the impacts of segregation on the mobility remain poorly understood and are overlooked in current rock-ice avalanche models. Here, we address modeling of segregation and its mobility feedback from both discrete and continuum points of view. Using the discrete element method, we simulate rock-ice avalanches, and the segregation that occur therein, as steady gravity-driven flows of particles different in size, density, and surface friction. Segregation results in sharp particle concentration gradients which, when coupled with the large surface friction difference between rocks and ice, lead to transitions in the flow kinematic profiles. We reveal that rocks and ice contact probabilities are key to modelling the effective friction and volume fraction of the mixture flows. Continuum equations are proposed to model the concentration dependence of the pressure, while segregation-induced flow velocity profiles are modelled using the non-local granular fluidity framework that accounts for microscopic frictional interactions. The findings are expected to promote more sophisticated modeling of rock-ice avalanches necessary for hazard risk reduction and mitigation.