A modular particle-continuum numerical method is used to simulate steady-state hypersonic flow over a hollow-cylinder-flare geometry. The resulting flowfield involves a mixture of rarefied nonequilibrium flow and high-density continuum flow. The hybrid particle-continuum method loosely couples direct simulation Monte Carlo and Navier-Stokes methods, which operate in different regions, use different mesh densities, and are updated using differentsized time steps. Hybrid numerical results are compared with full particle and full continuum simulations as well as with experimental data. The hybrid particle-continuum simulations are demonstrated to reproduce experimental and full particle simulation results for surface and flowfield properties including velocity slip, temperature jump, thermal nonequilibrium, heating rates, and pressure distributions with high accuracy. The hybrid method, which uses particle simulation next to the surface, is also shown to predict accurate heating rates even when a highly dissipative numerical scheme is used for the continuum solver. For this particular flow, a hybrid simulation is obtained with modest computational savings over full particle simulation.