In traditional integral equation method, conformal geometry discretization with adjacent edges or faces is very difficult to realize in case of complicated structures like composite conductor and dielectric. It will also lead to a very ill-conditioned matrix because of over-meshed elements. In this paper, a flexible, non-conformal geometry discretization scheme based on hybrid volume and surface integral equation is developed for meshing three-dimensional composite conductor and dielectric structures. For surface discretization of conductor, grid-robust higher order vector-basis functions are adopted. It keeps the flexibility of geometry modeling and reduces the number of the unknowns because of the property of point-basis functions. For volume discretization of dielectric, non-conformal volume-basis functions are used. Further, the integral equation-fast Fourier transformation algorithm is applied to expedite matrix–vector multiplication in iteration process. Some numerical results are given to demonstrate the accuracy and efficiency of this method. Because of truly full non-conformal discretization scheme, the present method has no difficulty of geometry discretization and has potential for structures with complicated geometry and materials. Copyright © 2012 John Wiley & Sons, Ltd.