Wrong multimeter readings measuring 12V lead acid battery
Situation: AC meter range reads double DC value when AC range is used for DC:

I have a meter of the same brand and very similar model (UT33B as opposed toU33C) and my meter behaves exactly as reported. Details at end. 

At one time it was extremely common for AC meter ranges on analog meters to read about double the correct value when DC was applied.
 What you are seeing is almost certainly somebody using the old style circuit.   

Battery voltages vary with state of charge and during charging and discharging. Nominal values may be quite different from actual value. eg


12V Lead acid - about 10V very flat to 13.7 V under normal charge and over 14V in some situations.
3.6V Lithium Ion - under 3V fully discharged and about 4.2V fully charged (per cell)
1.2V NimH - About 1.45V on charge when fully charged, 1.35 V just after charging., 1.3V fully charged after a while, 1.0 - 1.3 during discharge, under 1V sometimes when fully discharged.
NiCd - similar to NimH
AA Alkaline - 1.60 to 1.65V very new. 0.9 - 1.5V when discharging.
AA carbon zinc or heavy duty - 1.5V new. 0.9 - 1.5 discharging.




Update - reported results independently confirmed:

I recognised the meter from the picture :-).
 I bought a number of those a while ago to allow multiple simultaneous sanity check measurements on some equipment.  I just now checked the AC/DC behaviour with DC in and, as expected, results are as reported. As noted above, this is consistent with what I have seen in meters in the distant past. 

Applying a few semi random voltages to 200 VDC and 200 VAC ranges I get  

      2.9   5.9
      6.4  13.5
     11.9  25.6
     38.1  83.4


On 500 VDC / 500 VAC ranges the last voltage gave

     38  83


Slightly more than 2:1 and increasing slightly as Vin rises.
 I'll try to get around to tracing he circuit sometime soon.
 (3:30am now and morning appointment so ...)