We consider an SU(3)c'×SU(2)L'×U(1)Y' dark sector, parallel to the SU(3×SU(2×U(1 ordinary sector. The hypercharges, baryon numbers and lepton numbers in the dark sector are opposite to those in the ordinary sector. We further introduce three types of messenger sectors: (i) two or more gauge-singlet Dirac fermions, (ii) two or more [SU(2×SU(2)L']-bidoublet Higgs scalars, (iii) at least one gauge-singlet Dirac fermion and at least one [SU(2×SU(2)L']-bidoublet Higgs scalar. The lepton number conserving decays of the heavy fermion singlet(s) and/or Higgs bidoublet(s) can simultaneously generate a lepton asymmetry in the [SU(2]-doublet leptons and an opposite lepton asymmetry in the [SU(2)L']-doublet leptons to account for the cosmological baryon asymmetry and dark matter relic density, respectively. The lightest dark nucleon as the dark matter particle should have a mass about 5 GeV. By integrating out the heavy fermion singlet(s) and/or Higgs bidoublet(s), we can obtain three light Dirac neutrinos composed of the ordinary and dark neutrinos. If a mirror symmetry is further imposed, our models will not require more unknown parameters than the traditional type-I, type-II or type-I+II seesaw models.