Despite the highest specific capacity and lowest voltage of all secondary Li battery anode candidates, the application of Li metal anode has been a challenge due to dendritic Li electrodeposition in liquid electrolytes, leading to battery degradation and even safety issues. We previously generated a dendritic pattern map using a non-linear phase field model for a Li metal/liquid electrolyte binary system. However, the solid electrolyte interphase (SEI), the key to understand the mechanism of Li dendrite formation, is not explicitly included in the model. In this study, we hereby further advance our phase field model by incorporating the effect of SEI layer (or any artificial electrode protective coating layers (PCLs)) as an additional phase. A new set of phase-fields are re-defined to distinguish the spatial distribution of each individual phase in the electrode/SEI/electrolyte microstructure. Butler-Volmer type non-linear electrochemical kinetics and the SEI phase rigid body translation are tested to validate the new model. The impacts of different SEI properties (e.g. conductivity, Li diffusion coefficient, electron tunneling range, etc.) on Li plating and dendrite formation will be investigated. The possibility of incorporating the SEI mechanical effects on Li plating will also be discussed.