For absorption cooling cycles using water as a refrigerant, H2O/LiCl mixtures are suitable for replacing conventional H2O/LiBr mixtures. In addition, membrane devices can be used to develop compact and lighter absorption systems, and they can operate with H2O/LiCl mixtures. The present paper describes an experimental evaluation of a membrane desorber/condenser operating at atmospheric pressure. Two operation modes were analyzed: continuous cycle operation and intermittent operation. For the first operation mode, the maximum desorption rate was 3.49 kg/h·m2, with a solution temperature of 90.3 °C and a condensation temperature of 25.1 °C. The lowest desorption rate value was 0.26 kg/h·m2, with a solution temperature of 75.4 °C and a condensation temperature of 40.1 °C. In the second mode, after three operating hours, the refrigerant fluid produced, per 1 m2 of membrane area, 7.7, 5.6, 4.3, and 2.2 kg, at solution temperatures of 90.3, 85.3, 80.4, and 75.4 °C, respectively. A one-dimension heat and mass transfer model is presented. The calculated values of desorption rate and outlet temperatures were compared with the experimental data; a square correlation coefficient of 0.9929 was reached for the desorption rate; meanwhile, for the outlet solution temperatures and the outlet cooling-water temperatures, a square correlation coefficient up to 0.9991 was achieved. The membrane desorber has the advantages of operating at atmospheric-pressure conditions, high condensation temperature, the ability to use different saline solution working mixtures, and different operation methods. These advantages can lead to new absorption systems.