The broadband dielectric spectroscopy technique is applied, for the first time, to a composite material used as an electrode for lithium battery. The electrical properties (permittivity and conductivity) are measured from low (a few Hz) to microwave (a few GHz) frequencies. The results demonstrate that the broadband dielectric spectroscopy technique is very sensitive to the different scales of the electrode architecture involved in electronic transport, from interatomic distances to macroscopic sizes, as well as to the morphology at these scales, coarse or fine distribution of the constituents. This work opens up new prospects for a more fundamental understanding and more rational optimization of the electronic transport in composite electrodes for lithium batteries and other electrochemical energy storage technologies (including other batteries, supercapacitors, low-and medium-temperature fuel cells), electrochemical sensors and conductor-insulator composite materials.