We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the nonanomalous U(1) symmetry of the model. Our results are broadly consistent with large-Nc scaling and vector-meson dominance.