Granular systems are not always homogeneous and can be composed of grains with very different mechanical properties. To improve our understanding of the behavior of real granular systems, in this experimental study, we compress 2D bidisperse systems made of both soft and rigid grains. By means of a recently developed experimental set-up, from the measurement of the displacementfield we can follow all the mechanical observables of this granular medium from the inside of each particle up-to the whole system scale. We are able to detect the jamming transition from these observables and study their evolution deep in the jammed state for packing fractions as high as 0.915. We show the uniqueness of the behavior of such a system, in which way it is similar to purely soft or rigid systems and how it is different from them. This study constitutes thefirst step toward a better understanding of mechanical behavior of granular materials that are polydisperse in terms of grain rheology.