This paper presents a non-conformal volume surface integral equation (VSIE) for electromagnetic scatterings from composite structure consisting of perfect electric conductors (PEC) and inhomogeneous anisotropic materials with complex permittivity and permeability tensors. The VSIE can be decoupled into volume integral equation (VIE) and surface integral equation (SIE) for pentrable and non-pentrable scatterers respectively. The volume integral equation (VIE) is solved by applying the gradient-gradient operator on the Green's function which consequentially allows the use of piecewise constant non-conformal tetrahedral meshes. The surface integral equation (SIE) is solved using integral equation discontinuous Galerkin's (IEDG) formulation, which allows the PEC surface to be discretised using non-conformal meshes. The solution of VSIE consists of inner and outer loop solution process. During the inner solution loop, the scatterings from VIE domains and SIE domains are solved as independent domains. At the outer loop solution, their mutual interactions are computed. The iterative inner and outer loop solution is repeated until the solutions of the different domains have converged to the required accuracy.