The standard, time-of-flight method for measuring drift mobilities in semiconductors uses strongly absorbed illumination to create a sheet of photocarriers near an electrode interface. This method is problematic for solar cells deposited onto opaque substrates, and in particular cannot be used for hole photocarriers in hydrogenated amorphous silicon (a-Si:H) solar cells using stainless steel substrates. In this paper we report on the extension of the time-of-flight method that uses weakly absorbed illumination. We measured hole drift-mobilities on seven a-Si:H nip solar cells using strongly and weakly absorbed illumination incident through the n-layer. For thinner devices from two laboratories, the drift-mobilities agreed with each other to within a random error of about 15%. For thicker devices from United Solar, the drift-mobilities were about twice as large when measured using strongly absorbed illumination. We propose that this effect is due to a mobility profile in the intrinsic absorber layer in which the mobility decreases for increasing distance from the substrate.