The unsteady forces generated when a pump-jet propulsor operates behind a submarine hull are a major excitation source for hull vibration and radiated noise. Accurate prediction of these forces is therefore central to the design of low-noise propulsors. This study presents a numerical framework that couples the prediction of tonal forces via unsteady Reynolds-averaged Navier-Stokes (URANS) equations with the estimation of broadband forces using large eddy simulation (LES). The framework is applied to a model-scale pump-jet installed behind the SUBOFF hull. Numerical simulations characterize the unsteady forces on the rotor and stator blades, yielding their respective tonal and broadband force spectra. The results indicate that the tonal force and moment fluctuations occur predominantly at the first and the second blade passing frequency (BPF), while the broadband force and moment spectra exhibit a distinct hump around the first BPF.