It is well known that how to achieve broadband efficient acoustic absorption in a limited size range is still a great challenge. A composite structure has been proposed to address the problem of thicker dimensions of broadband microperforated plate (MPP) structures. This structure consists of MPP resonators with variable cross-section and variable depth of back cavities nested in a single-layer MPP back cavity. Firstly, the theoretical model of the built-in single-layer MPP resonator was established by using the transfer matrix. Then the width and cavity depth of the internal MPP resonator are finite element analyzed, and it is found that the cavity size of the internal MPP resonator has a great influence on the sound absorption performance of the structure. Taking advantage of the fact that the sound absorption performance is affected by the size of the built-in MPP resonator, absorbers with built-in MPP resonators of different sizes are combined in parallel. A composite structure with internal MPP resonators having different cross-sectional areas and unequal depths is designed. The results show that the composite MPP structure with a thickness of only 35 mm has an absorption efficiency of more than 80% in the frequency range of 575 Hz-1665 Hz. It provides some new ideas for the design of light and thin broadband MPP absorbers.