Two layers of molecular oligomers were deposited on flat carbon electrode surfaces by electrochemical reduction of diazonium reagents, then a top contact applied to complete a solid-state molecular junction containing a molecular bilayer. The structures and energy levels of the molecular layers included donor molecules with relatively high energy occupied orbitals and acceptors with low energy unoccupied orbitals. When the energy levels of the two molecular layers were similar, the device had electronic characteristics similar to a thick layer of a single molecule, but if the energy levels differed, the current voltage behavior exhibited pronounced rectification. Higher current was observed when the acceptor molecule was biased negatively in eight different bilayer combinations, and the direction of rectification was reversed if the molecular layers were also reversed. Rectification persisted at very low temperature (7 K), and was activationless between 7 and 100 K. The results are a dear example of a "molecular signature" in which electronic behavior is directly affected by molecular structure and orbital energies. The rectification mechanism is discussed, and may provide a basis for rational design of electronic properties by variation of molecular structure.