An efficient time-domain technique is proposed for multiscale electromagnetic simulations of layered structures. Each layer of a layered structure is independently discretized by finite elements, and the discontinuous Galerkin method is employed to stitch all discretized subdomains together. The hybrid implicit-explicit Runge-Kutta scheme combined with subdomain-based Gauss-Seidel iteration is employed for time stepping. The block Thomas algorithm is utilized to accelerate time stepping for block tri-diagonal systems, which are frequently encountered in discretized layered structures. Numerical examples demonstrate that the proposed method is efficient in simulating multiscale layered structures.