A front tracking method is developed for two-phase flows with surfactant-induced surface viscous effects using Level Contour Reconstruction Method (LCRM)[1]. LCRM is a hybrid front tracking approach that combines accurate surface tension calculation with robust handling of topological changes. The formulation incorporates surfactant transport, including surface diffusion and Marangoni stresses, together with surface viscous stresses arising from interfacial shear and dilatational viscosities. These stresses resist deformation due to velocity gradients tangential to the interface and interfacial compressibility effects, respectively. Surface rheology is modelled using the Boussinesq–Scriven constitutive law [2], which is implemented within the LCRM framework by exploiting the complementary strengths of front-tracking and level-set techniques. The numerical methodology is validated against benchmark problems involving drop deformation in imposed flows and buoyancy-driven drop rise, and wave-induced atomisation demonstrating excellent agreement with existing results and emphasising the necessity of rigorously accounting for surface viscous effects in interfacial dynamics. Since dilatational and shear surface viscosities are strongly correlated in Stokes flows, linearised models, and two-dimensional configurations, three-dimensional interfacial Faraday waves are finally investigated as a means of decoupling their respective contributions. Two dimensionless parameters are introduced: the Boussinesq number, which quantifies the relative importance of surface to bulk viscous stresses, and the ratio of dilatational to shear surface viscosity. While linear growth rates and instability thresholds are independent of this ratio, nonlinear analyses of square and hexagonal patterns reveal mode-dependent sensitivity. In particular, oblique modes experience enhanced damping for shear surface viscosity dominated interfaces, demonstrating that Faraday wave patterns provide a viable route for identifying and quantifying the distinct roles of dilatational and shear surface viscosities. [1] Panda, D., Shin, S., Abdal, A. M., Kahouadji, L., Chergui, J., Juric, D., & Matar, O. K. (2025). Direct numerical simulation of two-phase flows with surfactant-induced surface viscous effects. arXiv preprint arXiv:2509.24722. [2] Slattery, J. C., Sagis, L., & Oh, E. S. (2007). Interfacial transport phenomena. Boston, MA: Springer US.