Why do DMMs have a capacitor on their AC measurements?
A series capacitor acts as an high-pass filter, also known as AC-coupling capacitor. The reason is that for DC current, a capacitor is like an open circuit, whereas for higher frequencies (depending on C and the other resistances) it becomes more like a short circuit, if it's big enough.



The measurements will be indeed frequency dependent, but if the frequency is high enough the signal will fall in the right part of the curve, which is approximately flat.

So it's an useful tool, but to be used carefully. The same happens with scopes, where leaving the AC coupling on when measuring signals will distort them, like this square wave: