Thin, light-absorbing films attenuate the Raman signal of underlying substrates. In this article, we exploit this phenomenon to develop a contactless thickness profiling method for thin films deposited on rough substrates. We demonstrate this technique by probing profiles of thin amorphous silicon stripes deposited on rough crystalline silicon surfaces, which is a structure exploited in high-efficiency silicon heterojunction solar cells. Our spatially-resolved Raman measurements enable the thickness mapping of amorphous silicon over the whole active area of test solar cells with very high precision; the thickness detection limit is well below 1 nm and the spatial resolution is down to 500 nm, limited only by the optical resolution. We also discuss the wider applicability of this technique for the characterization of thin layers prepared on Raman/photoluminescence-active substrates, as well as its use for single-layer counting in multilayer 2D materials such as graphene, MoS2 and WS2.