A modular particle-continuum (MPC) method is extended to include internal energy nonequilibrium to simulate hypersonic steady-state flows that exhibit small regions of collisional nonequilibrium in a mainly continuum flow field. This method loosely couples an existing direct simulation Monte Carlo (DSMC) code to a Navier-Stokes solver (CFD) while allowing both time-step and cell size to be completely decoupled between each method. By limiting the size of the DSMC region to areas in collisional nonequilibrium, the MPC method is able to reproduce full DSMC results to within 5% while decreasing the computational time required by factors of 3 to 5. The goal of the present study is to incorporate rotational excitation in the hybrid method so that the size of the DSMC domain can be reduced. In addition, two vibrational relaxation methods are tested in the DSMC method. Results from full DSMC, full CFD, and the hybrid method are compared for both relaxation methods. It is found that having compatible relaxation models slightly improves flow field results. Further work on an adequate breakdown parameter for the prediction of collisional nonequilibrium may improve the accuracy and efficiency of the hybrid code.