Phase behavior in multi-component systems has a wide variety of applications in the chemical process industry. In this work, the interfaces in two-phase, three-component systems were modeled and studied. Direct calculations of the asymmetric concentration profiles near the critical points of fluid phase separation are very difficult since they are affected by mesoscopic fluctuations. In this study a "complete scaling" approach was used to model interfacial profiles for a highly asymmetric, dilute ternary mixture near the critical point of liquid-liquid separation. The symmetric order parameter profile, the density profile of the lattice gas model, was used to further calculate the asymmetric interfacial concentration profiles at the mesoscale. Fluid asymmetry has been introduced through mixing of the physical field variables into the symmetric scaling theoretical fields. The system-dependent mixing coefficients were calculated from experimental data and a mean-field equation of state, namely, the Margules model. The resultant interfacial profiles for the concentration of water across the methanol-rich and cyclohexane-rich phases show the asymmetry associated with the contribution of the entropy into the symmetric order parameter profile.