Suitable design of periodic metal/polymer composite materials is shown to facilitate resonant tunneling of light at absorbing wavelengths and to provide a means to significantly reduce optical absorption losses in polymer-based metallodielectric composite structures. The conditions for resonant tunneling are established based on the concept of "photonic band edge alignment" in 1D-periodic systems. For the particular case of a four-layer gold/polystyrene laminate structure, it is shown that the matching of the lower band edge of the 1D-periodic structure with the plasma frequency of the metal component facilitates the increase of optical transmission by about 500% as compared to monolithic film structures of equal total thickness. The effect of sheet thickness on the optical properties of thin metal films is determined and shown to be an important prerequisite for the reliable prediction of resonant metallodielectric structures. The resonant 1D-periodic metal/polymer heterostructures are shown to retain the flexural stability of the polymer matrix and thus could find application as flexible transparent conductors in areas such as "plastic electronics".