A dual air flow exchanger, enabling heat transfer and humidity transfer between two air flows, and including a plurality of air circulation networks stacked on each other along a stacking direction and separated in pairs by membranes permeable to water vapor and impermeable to air. At least one of the networks is made from a honeycomb structure with its two sides bearing on two of the membranes, the structure including cylindrical cells with axes parallel to the direction, and in which at least some of the cell faces are perforated to allow air passage.