This paper presents a comprehensive model for advanced membrane-based absorber components accounting for three separate fluid streams, one of them providing internal cooling, with complex flow patterns. The model was implemented with various liquid desiccants and their properties (including LiCl, CaCl2, and [emim][OMS] ionic liquid [IL]). The model has been validated using data from two laboratory prototype absorbers, one with CaCl2 as the working fluid and one with an IL as the working fluid. Entropy analysis was further carried out to verify the model and understand effect of internal cooling on the entropy variation of three fluid streams. The developed model and codes are expected to enable detailed configuration optimization and provide in-depth understanding of three-fluid heat and mass exchanger (HMX) performance. The paper also describes parametric studies of the HMX components in utilizing the latent heat removed in space cooling to heat water and numerically explores the unique benefit of its application in a semi-open absorption heat pump water heater. The results show that a single three-fluid HMX has the potential to achieve simultaneous dehumidification and water heating efficiently at cost effectiveness, particularly in hot and humid climates.