If you define frequency as the derivative of the phase with respect to time, then you also have an instantaneous frequency which (at least formally) also has Hz

If you define frequency as the derivative of the phase with respect to time, then you also have an instantaneous frequency which (at least formally) also has Hz as unit - even though it does not necessarily describe some real periodicity. To measure discrete events, I would prefer as unit "events per second" instead of Hz.