Measuring AC voltage from DC battery
When I am putting the multimeter probes in the same polarity with the
  battery, I am getting the AC voltage, but none if I put the probes in
  reverse polarity.


This is the clue to what is happening - "nothing" when you connect in reverse means that the meter uses a simple precision half wave rectifier to convert AC to a rational DC voltage. I'm guessing the meter makes no claims to measure RMS AC voltage - it assumes the AC voltage is a sine wave and, the output from the precision rectifier is averaged (with a filter) to give a "steady value" that is representative of the AC RMS value.

The problem is that this "steady value" will be about 50% of the AC RMS value and, if the inputted voltage is always at a peak value (because it is DC), then the steady-value will also be the peak value hence, with a 3 V battery, the steady-value measured by the meter is 3 V (the meter doesn't know any better and indicates that it is measuring a 6 V AC voltage).

If it were a 6V AC source it would see about 3V.