We propose an extension of the standard model (SM) by including a dark sector comprised of three generations of heavy right-handed neutrinos, a singlet scalar, and a singlet Dirac fermion, where the latter two particles are stable and are viable candidates of dark matter (DM). In the early Universe, the CP-violating out-of-equilibrium decay of heavy right-handed neutrinos to a singlet Dirac fermion and scalar in the dark sector generates a net DM asymmetry. The latter is then transported to the visible sector via a dimension-eight operator which conserves B-L symmetry and is in thermal equilibrium above the sphaleron decoupling temperature. An additional light singlet scalar is introduced which mixes with the SM Higgs and paves a path for annihilating the symmetric components of the DM candidates. We discuss the constraints on singlet-doublet Higgs mixing from invisible Higgs decay, signal strength at the LHC, and the direct search of DM at terrestrial laboratories. At tree level, the neutrinos are shown to be massless since the symmetry of the dark sector forbids the interaction of right-handed neutrinos with SM particles. However, at the one-loop level, the neutrinos acquire sub-eV masses as required by the oscillation experiments. © 2018 authors. Published by the American Physical Society.