The acoustical properties of double-leaf membranes, which are usually used as roofs in actual membrane-structure buildings, were theoretically analyzed. The double-leaf membranes were modeled, in the analysis, as of infinite extent. One of these leaves, which faces an incident sound, was assumed to have permeability, which is often the case in actual buildings. The permeability makes the acoustical performance of the double-leaf membranes totally different from that of impermeable double-leaf membranes in some cases. The effect on the absorptivity mainly appears at high frequencies: The optimal permeability can significantly increase the absorptivity at high frequencies, and makes the characteristics similar to those of cavity-backed porous absorbents. At low frequencies the effect also appears in a difference of absorption and transmission coefficients, which are consistently used in this paper to measure the absorptivity as the true energy loss caused in the structure. The transition of those two conditions, where a mass--spring peak appears or vanishes depending on the permeability, is at middle frequencies. These tendencies are drastically changed with changes in parameters such as mass of leaves, flow resistivity, cavity depth, etc. A detailed analysis was also carried out to interpret the mechanism and behavior of these effects.