This paper deals with a new configuration for a haptic system, which is able to simultaneously replicate independent force/displacement and force/area behaviors of a given material. Being force/area information a relevant additional haptic cue for improving softness discrimination, this system allows to extend the range of materials whose rheology can be carefully mimicked. Moreover, according to the Hertz theory, two objects with different curvature radius having the same force/displacement behavior can respond with different contact area to the same applied force. These behaviors can be effectively replicated by the integrated haptic system here proposed enabling and independent control of force/displacement and force/area. The system is comprised of a commercial device (Delta Haptic Device) serially coupled with a Contact Area Spread Rate (CASR) device. Two specimens of a material and two of another one, all with different curvature radii, were identified and modeled in terms of force/area and force/displacement. These behaviors were successfully tracked by the integrated haptic system here proposed.