We continue the development of high-order accurate thin layer approximations for time-domain electromagnetics and focus in this paper on a new family of models for thin transmission layers. The thin transmission layer approximations are valid for general isotropic materials and certain types of anisotropic materials. The models also allow the inclusion of smoothly curved layers. Both dielectric and magnetic materials can be considered. These models are non-trivial and we discuss their formulation, properties, and implementation in the context of discontinuous Galerkin methods which emerge as being particularly well suited for this family of models. The range of validity, accuracy, and stability of the models and numerical approximations is demonstrated through one- and two-dimensional examples. (C) 2010 Elsevier B.V. All rights reserved.