The microscale liquid flow in nanoscale systems considering slip boundary has been widely studied in recent years, however, they are limited to single-phase flow. As in nature, multicomponent and multiphase flows can also exist with non-zero slip velocities, such as oil/water slip flow in nanoporous shale. In this paper, a novel multicomponent-multiphase multiple-relaxation-time lattice Boltzmann method with a combinational slip boundary condition is developed to study the two-phase slip flow behaviors. The proposed combined slip boundary condition is derived from adjustments to the conventional diffusive Maxwell’s reflection and half-way bounce-back scheme boundary parameters, incorporating a compelled conservation requirement. With the analysis of simulations for the layer, slug, and droplet types of two-phase flow in single pores, and two-phase flow in porous media with complex wall geometry, it can be concluded that the proposed schemes of two-phase slip boundary conditions are particularly suitable for multicomponent and multiphase flow with a non-zero slip velocity. The proposed model can be used to determine relative permeability and simulate spontaneous imbibition in particular in shale reservoirs where those flow properties are hard-to-determine.