Assembly interfaces between dissimilar materials widely exist in thermal protection structures of hypersonic aircrafts. The resulting imperfect contact and thermomechanical coupling need to be carefully considered in structural analyses. Since the traditional three-dimensional finite element method is computational expensive and inefficient, a new zonal coupled continuous/discontinuous Galerkin finite element method is established especially for the thermal and thermomechanical analyses of problems with dissimilar-material assembly interfaces. The effects of material nonlinearity, temperature, and stress-dependent thermal contact resistance to the structural thermomechanical coupling response are taken into account. In addition, an efficient and accurate finite element software suitable for large-scale engineering computations and three-dimensional thermal and thermomechanical coupling analyses of problems with dissimilar-material assembly interfaces is developed. This software provides a research tool and technical supports for the aerothermoelasticity prediction and safety evaluation of novel hypersonic aircrafts.