Internal resistance of a battery
You made it too complicated. The battery current is 0.5A, as you said. That 0.5A is causing a 0.5V drop in the battery voltage due to the combined series resistance of the batteries. We can just use Ohm's law. Vdrop = Ibatt * Rbatt.

So, Rbatt = 0.5V / 0.5A = 1 Ohm. But that is the combined series resistance. So each battery contributes 0.5 Ohms to the total.