A new nodal interface diffusion equation is derived by applying the second form of Green’s theorem to the transverse-integrated diffusion equation. By virtue of this integral equation, a unified theory of the nodal interface partial current method and the nodal interface net current or flux method is established. Use of the infinite-medium Green’s function in that equation results in the same interface partial current equation as the nodal Green’s function method. The nodal interface net current equation can be proven to converge and demonstrates a computational efficiency superior to the nodal interface partial current method for standard benchmark problems.