In this paper, an efficient volume surface integral equation (VSIE) method with nonconformal discretization is developed for the analysis of electromagnetic scattering from composite metallic and dielectric (CMD) structures. This VSIE scheme utilizes curved tetrahedral (triangular) elements for volume (surface) modeling and the associated CRWG (CSWG) basis functions for volume current (surface) current modeling. Further, a discontinuous Galerkin (DG) volume integral equation (VIE) method and a DG surface integral equation (SIE) approach are adopted for dielectric and metallic parts, respectively, which allow both conformal and nonconformal volume/surface discretization improving meshing flexibility considerably. Numerical results are provided to demonstrate the accuracy, efficiency, and flexibility of our scheme.