  We present a detailed study of a combined singlet-doublet fermion and triplet
scalar model for dark matter. These models have only been studied separately in
the past. Together, they form a simple extension of the Standard Model that can
account for dark matter and explain the existence of neutrino masses, which are
generated radiatively. This holds even if singlet-doublet fermions and triplet
scalars never contribute simultaneously to the dark matter abundance. However,
this also implies the existence of lepton flavour violating processes. In
addition, this particular model allows for gauge coupling unification. The new
fields are odd under a new $\mathbb{Z}_2$ symmetry to stabilise the dark matter
candidate. We analyse the dark matter, neutrino mass and lepton flavour
violation aspects both separately and in conjunction, exploring the viable
parameter space of the model. This is done using a numerical random scan
imposing successively the neutrino mass and mixing, relic density, Higgs mass,
direct detection, collider and lepton flavour violation constraints. We find
that dark matter in this model is fermionic for masses below about 1 TeV and
scalar above. The narrow mass regions found previously for the two separate
models are enlarged by their coupling. While coannihilations of the weak
isospin partners are sizeable, this is not the case for fermions and scalars
despite their often similar masses due to the relatively small coupling of the
two sectors, imposed by the small neutrino masses. We observe a high degree of
complementarity between direct detection and lepton flavour violation
experiments, which should soon allow to fully probe the fermionic dark matter
sector and at least partially the scalar dark matter sector.
