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A new representation of the 2N fold integrals appearing in various two-matrixmodels that admit reductions to integrals over their eigenvalues is given interms of vacuum state expectation values of operator products formed fromtwo-component free fermions. This is used to derive the perturbation series forthese integrals under deformations induced by exponential weight factors in themeasure, expressed as double and quadruple Schur function expansions,generalizing results obtained earlier for certain two-matrix models. Links withthe coupled two-component KP hierarchy and the two-component Toda latticehierarchy are also derived.Comment: Submitted to: "Random Matrices, Random Processes and Integrable  Systems", Special Issue of J. Phys. A, based on the Centre de recherches  mathematiques short program, Montreal, June 20-July 8, 200

Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions