We present a new non-combinatorial interpretation for the fermionic nature of the 2D dimer problem. The partition functions of the closed-packed dimer models settled on the most general inhomogeneous rectangular, triangular, and hexagonal lattice nets are obtained as fermionic Gaussian integrals. These Gaussian representations provide the analytic results for the partition functions and dimer-dimer correlations for a variety of regular lattices, and can also be applied to analyse defects, boundary influences, effects of disorder, etc., in dimer models.