If the batteries are in series, then they both get EXACTLY the same charging current, if the voltages across the batteries are different, then you either have a faulty battery, or simply that one is already charged to a much higher level than the other. But at 0.6V, it looks more like a duff battery.
If it'll make you happier, swap the two batteries round, the 'first' one will then read 0.6V, and the 'second' 1.5V.
I presume you have the solar panel outside in direct bright sunlight?, and even at that it will take a long time to charge the batteries.