Either input pin can be given a positive or negative voltage with respect to the other input pin, so I suppose you would say that the op-amp can work with AC signals. But the op-amp can also amplify an unchanging DC difference between the two inputs. read more
The polarity remains constant in a headphone, thus strictly speaking a headphone runs DC. However, the definition of DC is often extended to the constant, zero-frequency, or slowly varying local mean value of a voltage or current, if you consider the extended definition, headphones runs neither DC or AC. read more