[en] I present a theoretical analysis of the phase diagram of bilayer Josephson junction arrays in the presence of charge and magnetic frustration. Using a dual description I show that the fundamental constituents of this theory are electric and magnetic excitations and that their condensations lead to a plethora of possible phases. The new formulation points out to the emergence of a rich phase diagram not attainable by standard mean field theory approaches. In addition to the usual superconducting and insulating states in the bilayer system, I find states exhibiting Hall quantization coexisting with interlayer coherence, states with Hall quantization without interlayer coherence and interlayer coherent states without Hall quantization