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Transient electromagnetic scattering by composite structures is formulated by time-domain combined field integral equations (TDCFIEs). Traditionally, the TDCFIEs are solved by combining the method of moments (MoMs) in space domain and march-on-intime (MoT) scheme in time domain. The space-domain MoM requires two basic functions to represent the electric and magnetic current densities on material interfaces, respectively, and the conventional choice of \hat n\times \mathrm RWG basis function for representing the magnetic current density may not be good in the TDCFIEs. In addition, the MoT scheme has a well-known late-time instability problem, which will aggravate in the surface integral equations with penetrable media. In this communication, the TDCFIEs for composite structures are solved by a different approach in which the Nyström method is used to discretize the space domain, while the Galerkin method with Laguerre basis and testing functions is employed to discretize the time domain. The proposed approach can fully overcome the drawbacks of the traditional approach as demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]