The paper concerns the sound absorption performance of a compound absorber which consists of a parallel arrangement of multiple perforated panel absorbers of different backing cavity depths partially filled with poroelastic polymer materials. Three polymer materials are considered: expandable polystyrene (EPS) foam, polymethacrylimide (PMI) foam, and polyester fiber. The normal incidence sound absorption coefficients of the compound panel absorber are tested experimentally. Results show that the former two foams can achieve similar absorption performance to the rigid cavity configuration, while the resonances shift to lower frequencies due to the changes of effective cavity depths. It is also found that the additional attenuation by polymer foams may improve sound absorption, but the effect is marginal. For polyester fiber, results show that it performs more like a single perforated panel absorber. Finite element simulation of the compound panel absorber is also discussed, and good agreement is observed between simulated and experimental results.