The interaction of kHz μs-pulsed atmospheric pressure He jets with metallic targets is studied through simulations and experiments, focusing on the differences between floating and grounded targets. It is shown that the electric potential of the floating target is close to grounded in the instants after the impact of the discharge, but rises to a high voltage, potentially more than half of the applied voltage, at the end of the 1 μs pulse. As a result, a return stroke takes place after the discharge impact with both grounded and floating targets, as a redistribution between the high voltage electrode and the low voltage target. Electric field, electron temperature and electron density in the plasma plume are higher during the pulse with grounded target than with floating target, as gradients of electric potential progressively dissipate in the latter case. Finally, at the fall of the pulse, another electrical redistribution takes place, with higher intensity with the highly-charged floating target than with the grounded target. It is shown that this phenomenon can lead to an increase in electric field, electron temperature and electron density in the plume with floating target.