Replicating nacre's multiscale architecture represents a promising approach to design artificial materials with outstanding rigidity and toughness. It is highly desirable yet challenging to incorporate self-healing and shape-programming capabilities into nacre-mimetic composites due to their rigidity and high filler content. Here, we report such a composite obtained by infiltrating a thermally switchable Diels-Alder network polymer into a lamellar scaffold of alumina. The chemical bond switchability and the physical confinement by the filler endows the composite with sufficient molecular mobility without compromising its thermal dimension stability. Consequently, our composite is capable of self-healing internal damages. Additionally, in contrast to the intractable planar shape of other artificial nacres, precise control of the polymer chain dynamics allows the shape of our composite to be programmed permanently via plasticity and temporarily via shape memory effect. Our approach paves a new way for designing durable multifunctional bioinspired structural materials.