A significant charge transfer, which differs from tunneling, over thick AlxGa1-xAs barrier in GaAs/AlxGa1-xAs asymmetric double quantum wells is studied by cw photoluminescence excitation (PLE) and time-resolved photoluminescence. It is found that 300-Angstrom-thick Al0.3Ga0.7As barrier is universally ''leaky'' with transport time of similar to 300 ps, while AlAs and AlAs/GaAs digital alloy barriers with same thickness are not. Aided by a model calculation, we suggest that the intrinsic inhomogeneities in the alloy, which recent x-ray and scanning tunneling microscope studies revealed, may be responsible.