Protons and electrons are being exploited in different natural charge transfer processes. Both types of charge carriers could be, therefore, responsible for charge transport in biomimetic self-assembled peptide nanostructures. The relative contribution of each type of charge carrier is studied in the present work for fibrils self-assembled from amyloid-β derived peptide molecules, in which two non-natural thiophene-based amino acids are included. It is shown that under low humidity conditions both electrons and protons contribute to the conduction, with current ratio of 1:2 respectively, while at higher relative humidity proton transport dominates the conductance. This hybrid conduction behavior leads to a bimodal exponential dependence of the conductance on the relative humidity. Furthermore, in both cases the conductance is shown to be affected by the peptide folding state under the entire relative humidity range. This unique hybrid conductivity behavior makes self-assembled peptide nanostructures powerful building blocks for the construction of electric devices that could use either or both types of charge carriers for their function.