  We present transport measurements performed in InAs/GaSb double quantum
wells. At the electron-hole crossover tuned by a gate voltage, a strong
increase in the longitudinal resistivity is observed with increasing
perpendicular magnetic field. Concomitantly with a local resistance exceeding
the resistance quantum by an order of magnitude, we find a pronounced non-local
resistance signal of almost similar magnitude. The co-existence of these two
effects is reconciled in a model of counter-propagating and dissipative quantum
Hall edge channels providing backscattering, shorted by a residual bulk
conductivity.
