GaAs/AlAs single quantum well structures designed with well thickness near the type-I/type-II crossover show distinctive photoluminescence peaks corresponding to both type-I and type-II recombinations. Photoluminescence measurements as a function of applied electric field and temperature ranging from 23 to 180 K and current-voltage measurements are presented for two MBE-grown structures clad with Si-doped Al0.45Ga0.55As layers on n+-GaAs [100] substrates. The large and field-dependent energy separation between type-I and type-II luminescence peaks is understood to arise from the build-up of electrons at the X point in the AlAs barrier.