Reconfigurable tactile displays are being used to provide refreshable Braille information; however, the delivered information is currently limited to an alternative of Braille because of difficulties in controlling the deformation height. Herein, we present a photothermally activated polymer-bilayer-based morphable tactile display that can programmably generate tangible three-dimensional topologies with varying textures on a thin film surface. The morphable tactile display was composed of a heterogeneous polymer structure that integrated a stiffness-tunable polymer into a light-absorbing elastomer, near-infra-red light-emitting diode (NIR-LED) array, and small pneumatic chamber. Topological expression was enabled by producing localized out-of-plane deformation that was reversible, height-adjustable, and latchable in response to light-triggered stiffness modulation at each target area under switching of stationary pneumatic pressure. Notably, the tactile display could express a spatial softness map of the latched topology upon re-exposing the target areas to modulated light from the NIR-LED array. We expect the developed tactile display to open a pathway for generating high-dimensional tactile information on electronic devices and enable realistic interaction in augmented and virtual environments.