An alternator in a car provides
all the current needed for everything except the starter motor. As soon as the car is started, the alternator begins to replenish the charge removed from the battery by the starter motor (assuming a successful engine start) while providing additional current at a regulated voltage to operate everything else. So, as
@BobK said, you cannot discharge and charge a battery at the same time.
You discharge when there is no
other power source available for charging. When a power source does become available, i.e., the alternator from a running engine or some other source of electricity, you re-charge the battery with whatever current is available to do so. If there isn't enough current available to re-charge the battery, then it will continue to discharge into the load, adding its current to whatever the external power source is providing.
A common example of this is a solar-operated walk light consisting of (typically) a NiCd cell, a solar voltaic cell, an LED and some electronics. During the day the electronics keeps the LED off while the solar voltaic cell powers the electronics and charges the NiCd cell. At night, the NiCd cell powers the LED. Now imagine the electronics is eliminated and the solar voltaic cell powers
both the LED and the NiCd cell (you can make one of these yourself!). During the day the solar voltaic cell (it's big enough!) lights up the LED
and charges the battery. As the sun goes down, the solar voltaic cell current drops and the LED begins drawing current from the battery as well as from the solar voltaic cell. Eventually there is not enough current from the solar voltaic cell (it's dark outside) to light the LED
or charge the NiCd cell. However, the NiCd cell has been charging all day from power supplied by the solar voltaic cell, so at night the NiCd cell provides
all the LED current.
If daylight doesn't occur again soon enough, the NiCd will become completely depleted, the LED will go out, and everything must wait for enough sunlight before resuming operation. It doesn't make any sense to operate the little LED in daylight, so most of these lights have an electronic circuit that blocks current to the LED when the solar voltaic cell is sufficiently illuminated. Some even use an LDR (light dependent resistor) for this purpose. But in no case do electrons ever leave the circuit, and the NiCd cell is never charging and discharging at the same time.
