Human tactile perception of materials relies on complex multisensory touch cues, yet the relationship between low-level tactile signals and perceptual representations remains poorly understood. This knowledge gap hinders the integration of touch in digital environments and the development of robots capable of human-like tactile perception. Here, we present an interpretable computational framework for modeling human material perception and recognition using multisensory touch data. Our framework comprises three interconnected models: Model 1 maps finger-surface interaction features to psychophysical sensory attributes, Model 2 classifies materials based on these perceptual representations, and Model 3 directly classifies materials from tactile features. The results showed that combining information from pressing, static contact, and sliding interactions improves prediction accuracy, and that thermal cues are particularly informative for both perceptual modeling and material classification. These findings highlight the importance of thermal and compliance cues, which remain underrepresented in current robotic fingers and haptic displays. Incorporating such cues may enhance artificial systems' ability to approximate human material perception and guide the design of more perceptually grounded haptic interfaces.