Historically, the methods used to describe the electromagnetic response of random, three-dimensional (3D), metal-dielectric composites (MDCs) have been limited to approximations such as effective-medium theories that employ easily-obtained, macroscopic parameters. Full-wave numerical simulations such as finite-difference time domain (FDTD) calculations are difficult for random MDCs due to the fact that the nanoscale geometry of a random composite is generally difficult to ascertain after fabrication. We have developed a fabrication method for creating semicontinuous metal films with arbitrary thicknesses and a modeling technique for such films using realistic geometries. We extended our two-dimensional simulation method to obtain realistic geometries of 3D MDC samples, and we obtained the detailed near- and far-field electromagnetic responses of such composites using FDTD calculations. Our simulation results agree quantitatively well with the experimentally measured far-field spectra of the real samples.