By using different widths for two AlAs quantum wells comprising a bilayer system, we force the X-point conduction-band electrons in the two layers to occupy valleys with different Fermi contours, electron effective masses, and g factors. Since the occupied valleys are at different X points of the Brillouin zone, the interlayer tunneling is negligibly small despite the close electron layer spacing. We demonstrate the realization of this system via magnetotransport measurements and the observation of a phase-coherent, bilayer nu=1 quantum Hall state flanked by a reentrant insulating phase.