We show experimentally that thin membrane-type acoustic metamaterials can serve as a total reflection nodal surface at certain frequencies. The small decay length of the evanescent waves at these frequencies implies that several membrane panels can be stacked to achieve broad-frequency effectiveness. We report the realization of acoustic metamaterial panels with thickness ≤15 mm and weight ≤3 kg/m2 demonstrating 19.5 dB of internal sound transmission loss (STL) at around 200 Hz, and stacked panels with thickness ≤60 mm and weight ≤15 kg/m2 demonstrating an average STL of >40 dB over a broad range from 50 to 1000 Hz.