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Molecular membranes in aqueous solutions interact via van der Waals, hydration, and electrostatic forces. In addition, thermal fluctuations of the membranes generate long-range effective repulsion. A systematic theory of the interplay among these interactions reveals a continuous phase transition from a state where the membranes are bound together to a state where they are completely separated. In three dimensions, this unbinding transition is driven by fluctuations. Quantitative correlations with data for lipid bilayers suggest that it can be observed experimentally.