The paper is about the interpretation and separability of the effective permittivity in case that both the permittivity and the conductivity are dispersive and thus complex-valued. It is shown that: a) it is always possible to retrieve the static conductivity and the high-frequency (optical) permittivity from the effective permittivity; b) it is in general not possible to separate the complex conductivity from the complex permittivity. The findings rely on the application of the Hilbert transform and their effectiveness is verified by means of a numerical example.