The ever-emerging mobile market induced a blooming interest in stylus-based interactions. However, most state-of-the-art styli are passive or display only unimodal tactile feedback. Multimodal haptic devices that simultaneously stimulate our cutaneous and kinesthetic receptors to provide immersive and realistic sensations in a virtual environment during touchscreen interactions are highly desired. To this end, we developed FeelPen, a novel handheld multimodal haptic interface for touchscreens, incorporating various actuators in a smartly designed way. A voice-coil actuator, placed along the stylus tip, simulates object compliance by modifying its stroke force. Electrovibration, generated between the stylus tip and a capacitive screen, delivers roughness and stickiness cues. In addition, temperature feedback on the fingertip is provided by a miniature thermal module. We conducted characterization experiments to determine the physical characteristics and limitations of the device, followed by a psychophysical experiment, where the perceptual dimensions of the device were extracted using the semantic differential method on a set of artificial textures. Our results revealed four tactile dimensions, with the first two related to texture surface properties, and the third and fourth dimensions linked to material softness and coldness, respectively. FeelPen opens up new dimensions for future realistic texture rendering on touchscreens.