The broadband dielectric spectroscopy (BDS) technique (40 to 1010 Hz) is used here to measure the electronic transport across all observed size scales of a Li1.1V3O8-polymer-gel composite material for lithium batteries. Different electrical relaxations are evidenced, resulting from the polarizations at the different scales of the architecture: (i) atomic lattice (small-polaron hopping), (ii) particles, (iii) clusters of particles, and finally (iv) sample-current collector interface. A very good agreement with dc-conductivity measurements on a single macro-crystal [M. Onoda and I. Amemiya, J. Phys.: Condens. Matter, 2003, 15, 3079.] shows that the BDS technique does allow probing the bulk (intrinsic) electrical properties of a material in the form of a network of particles separated by boundaries in a composite. Moreover, this study highlights a lowering of the surface electronic conductivity of Li1.1V3O8 particles upon adsorption of polar ethylene carbonate (EC) and propylene carbonate (PC) that trap surface polarons. This result is meaningful as EC and PC are typical constituents of a liquid electrolyte of lithium batteries. It is thus suggested that interactions between active material particles and the liquid electrolyte play a role in the electronic transport within composite electrodes used in a lithium battery.