The seismoelectric and self-potential methods are showing promises to characterize both the vadose zone of the Earth, hydrocarbon reservoirs and CO2 sequestration. That said, the dependence of a key parameter, the streaming coupling coefficient, with the saturation remains highly debated. We explore here the relationship between the streaming potential coupling coefficient, the electrical resistivity, the capillary pressure curves and the permeability in two saturated and partially saturated carbonate rocks characterized by distinct textures. We investigate a limestone from the Paris basin (the Brauvilliers limestone) and a dolostone from the Aquitain basin (sample labeled LS2), both in France. The two core samples are characterized in terms of their porosity and intrinsic formation factor. A new core flooding system is used to measure simultaneously and, for the first time, both the relative permeability, the resistivity index and the streaming potential coupling coefficient in steady-state two-phase flow conditions as a function of the saturation with CO2 or N2. The results are compared with a recently developed theoretical model, which can accommodate either the Brooks and Corey model or the van Genuchten model for the capillary pressure curves. This model is predicting a set of relationships between the streaming potential coupling coefficient, the relative permeability and the second Archie's exponent. We found a good agreement between the model based on the van Genuchten approach and experimental data, but still we could not fit all the curves with the same value of the pore size index λ or van Genuchten exponent mv especially for the relative permeability.