The hybrid volume and surface integral equation approach is applied to solve electromagnetic scattering and radiation problems involving conducting and/or dielectric objects. To flexibly and accurately model the complex structures and reduce the number of unknowns, mixed mesh scheme is developed to discretize the object. In this scheme, the triangles and quadrangles are used to discretize the conducting part of the object, and the tetrahedrons, hexahedrons, prisms and pyramids are used to model the dielectric volumes of the scatterer. Numerical results showed the solution accuracies from the mixed element meshes are of the same level compared with the single element meshes, but uses much less number of unknowns. This leads to flexibility for mesh generating and reduces the use of computing resources.