A bstract We present a detailed study of a combined singlet-doublet scalar and singlet-doublet fermion model for dark matter. These models have only been studied separately in the past. We show that their combination allows for the radiative generation of neutrino masses, but that it also implies the existence of lepton-flavour violating (LFV) processes. We first analyse the dark matter, neutrino mass and LFV aspects separately. We then perform two random scans for scalar dark matter imposing Higgs mass, relic density and neutrino mass constraints, one over the full parameter space, the other over regions where scalar-fermion coannihilations become important. In the first case, a large part of the new parameter space is excluded by LFV, and the remaining models will be probed by XENONnT. In the second case, direct detection cross sections are generally too small, but a substantial part of the viable models will be tested by future LFV experiments. Possible constraints from the LHC are also discussed.