This study investigates sound absorption performance of a kind of wideband micro-perforated panel (MPP) absorbers with parallel-arranged backing cavities at different depths in a diffuse field. An analytical prediction model is presented for evaluating the random incidence absorption coefficient of this type of absorbers, and it exhibits excellent agreement with finite element model and experimental measurements. Then, numerical cases were established using this model to investigate the absorption characteristics of this type of absorbers under random incidence, considering the influence of cavity depths and MPP parameters. Results show that the cavity depth and MPP perforation diameter in this absorber are primary influencing parameters controlling the overall sound absorption performance. Cavities at different depths introduce multiple resonant absorption peaks, while the perforation diameter determines matching conditions between the MPP and air impedance, which simultaneously broaden the absorption bandwidth of this MPP absorber. Although individually adjusting the panel thickness and perforation rate has a smaller impact compared to the perforation diameter, the interaction between these two parameters has significant influences across the entire absorption frequency band.