We report the mechanism for simultaneous realization of acoustic perfect absorption (PA) and broadband insulation (BI) in the acoustic free field by a layered acoustic metamaterial (LAM). The proposed LAM comprises two critically coupled membrane-type acoustic metamaterials sandwiching a porous material layer. Both theoretical and experimental results verify that the proposed LAM sample can achieve nearly PA (98.4% in experiments) at 312 Hz with a thickness of 15 mm (1/73 of wavelength) and BI in the frequency range of 200–1000 Hz with an areal density of 2.2 kg/m2. In addition, the real parts of both the effective dynamic density and bulk modulus reach zero precisely at the critical frequency of 312 Hz, arising from the monopolar eigenmode of LAM. Our work advances the concept of synthetic design of sound absorption and insulation properties of multi-impedance-coupled acoustic systems and promotes membrane-type acoustic metamaterials to more practical engineering applications.

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