We calculate the Hall transport in a multiband system with a dominant interband interaction between carriers having electron and hole character. We show that this situation gives rise to an unconventional scenario, beyond the Boltzmann theory, where the quasiparticle currents dressed by vertex corrections acquire the character of the majority carriers. This leads to a larger (positive or negative) Hall coefficient than what may be expected on the basis of the carrier balance, with a marked temperature dependence. Our results explain the puzzling measurements in pnictides and provide a more general framework for transport properties in multiband materials.