A generalized extension of Flory-Rehner (FR) theory is derived to describe equilibrium swelling of polymer networks, including copolymers with two or more chemically distinct repeat units, in either pure or mixed solvents. The model is derived by equating the chemical potential of each solvent in the liquid and gel phases at equilibrium, while assuming the deformation of the network chains is affine. Simplifications of the model are derived for specific cases involving homopolymer networks, copolymer networks, pure solvents, and binary solvent mixtures. With reasonable assumptions, the number of polymer-solvent interaction parameters that must be determined by experiments can be reduced to two effective parameters (θ1 and θ2), which describe the net interactions between water/copolymer (θ1) and ethanol/copolymer (θ2), respectively. Experimental measurements of the swelling of random copolymer networks of n-butyl acrylate and 2-hydroxyethyl acrylate in water, ethanol, and a 100 g/L ethanol/water mixture are utilized to validate the model. For a random copolymer network, θ1 and θ2 can be obtained by fitting the three-component FR model to equilibrium swelling data obtained in the pure solvents. Predicted solvent volume fractions for swelling in water-ethanol mixtures obtained by inserting fitted values of θ1 and θ2 into the four-component FR model are in reasonable agreement with experimental measurements.