The effect of thickness and molecular structure on the probability of electron tunneling through water layers is investigated using a recently developed method. Water configurations of 1-4 layers are prepared between two parallel slabs of the Pt(100) surface, using equilibrium molecular dynamics and the polarizable simple point charge water model. Electron tunneling probabilities through the different water layers are computed as functions of energy using the absorbing boundary conditions Green function method and employing either an effective two-body water-electron interaction or a many-body polarizable water-electron potential. As long as the electron incident energy is below the barrier and far from a resonance state, the tunneling probabilities can be reasonably fitted to a one-dimensional rectangular-barrier model. However, near and over-barrier transmission probabilities cannot be reasonably described using a one-dimensional model, and the three-dimensional discrete structure of the water plays an important role. In all systems, the many-body electronic polarizability of the water significantly affects the transmission probability. The role played by the first adsorbed water layer is also discussed.