The forward-backward charge asymmetries of theb andc quarks are measured with the JADE detector at PETRA at s√=35 GeV and 44 GeV using both electrons and muons to tag the heavy quarks. At s√=35 GeV, a simultaneous fit for the two asymmetries yields the resultA b =−9.3±5.2% (state.) ndA c =−9.6±4.0% (stat.). The systematic errors are comparable with the statistical uncertainties. Combining the measurements at both energies and alternately constraining the weak coupling of thec andb quark to their Standard Model values (a c =1,a b =−1) increases the precision of the measurement of coupling constant of the other quark. Using this procedurea b =−0.72±0.34 anda c =0.79±0.40, where the numbers are corrected for BBˉ−mixing and the errors include both statistical and systematic contributions. The mixing parameter for continuum bbˉ−production is determined to be χ-0.24±0.12 if both heavy quark coupling constants are constrained to their values in the Standard Model.