A fully kinetic particle-in-cell model combined with a nonhomogeneous interface immersed finite element field solver is presented for simulations of the plasma charging at the lunar terminator. This model explicitly includes the lunar regolith layer and the bedrock in the simulation domain, taking into account of regolith layer thickness and permittivity, and is capable of resolving a nontrivial surface terrain or spacecraft configuration. Simulations are presented to study surface charging and lunar outpost charging at the lunar terminator region. The results suggest that substantial differential charging can develop, even under a very moderate plasma charging environment.