The quasiparticle spectra of atomically thin semiconducting transition metal dichalcogenides (TMDCs) and their response to an ultrafast optical excitation critically depend on interactions with the underlying substrate. Here, we present a comparative time- and angle-resolved photoemission spectroscopy (TR-ARPES) study of the transient electronic structure and ultrafast carrier dynamics in the single- and bilayer TMDCs MoS2 and WS2 on three different substrates: Au(111), Ag(111) and graphene/SiC. The photoexcited quasiparticle bandgaps are observed to vary over the range of 1.9-2.5 eV between our systems. The transient conduction band signals decay on a sub-50 fs timescale on the metals, signifying an efficient removal of photoinduced carriers into the bulk metallic states. On graphene, we instead observe a fast timescale on the order of 170 fs, followed by a slow dynamics for the conduction band decay in MoS2. These timescales are explained by Auger recombination involving MoS2 and in-gap defect states. In bilayer TMDCs on metals we observe a complex redistribution of excited holes along the valence band that is substantially affected by interactions with the continuum of bulk metallic states.