We consider fast and accurate solutions of scattering problems involving multiple dielectric and composite dielectric-metallic structures with three-dimensional arbitrary shapes. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE), which produces well-conditioned matrix equations. Equivalent electric and magnetic surface currents are discretized by using the Rao-Wilton-Glisson (RWG) functions defined on planar triangles. Matrix equations obtained with JMCFIE are solved iteratively by employing a Krylov subspace algorithm, where the required matrix- vector multiplications are performed efficiently with the multilevel fast multipole algorithm (MLFMA). We also present a four-partition block-diagonal preconditioner (4PBDP), which provides efficient solutions of JMCFIE by reducing the number of iterations significantly. The resulting implementation based on JMCFIE, MLFMA, and 4PBDP is tested on large electromagnetics problems.