The cotton-based composite is equipped with a single/double semipermeable membrane made of polyurethane (PU) (100%), which blocks liquid transport to the surrounding environment. The complex problem analyzed involves the coupled transport of water vapor within the textile material, transport of liquid water in capillaries, as well as heat transport with vapor and liquid water. The problem can be described using the mass transport equation for water vapor, heat transport equation, and mass transport equation for liquid moisture, accompanied by the set of corresponding boundary and initial conditions. State variables are determined using a complex multistage solution procedure within the selected points for each layer. The distributions of state variables are determined for different configurations of membranes.