The sample of hadronic Z decays collected by the ALEPH detector at LEP in the years 1991-1995 is analysed in order to measure the forward-backward asymmetry in Z → bb̄ and Z → cc̄ events and the B 0 -B̄ 0 average mixing parameter χ̄. Quark charges are tagged by the charges of electrons and muons produced in b and e semileptonic decays. Multivariate analyses are used to separate the event flavours and b → ℓ/b → c → ℓ processes. The b and c quark asymmetries are measured simultaneously; the average mixing parameter and the pole asymmetries are determined to be χ̄ = 0.1196 ± 0.0049 (stat.) -0.0050+0.0043 (syst.), A FB0,b = 0.0998 ± 0.0040 (stat.) ± 0.0017 (syst.), A FB0,c = 0.0732 ± 0.0053 (stat.) ± 0.0037 (syst.). These asymmetries, combined with the ALEPH measurements of the b asymmetry using inclusive b hadron decays and of the c asymmetry using reconstructed D mesons, correspond to a value of the effective electroweak mixing angle of sin 2 θ Weff = 0.23188 ± 0.00046.