A component (10) for a gas turbine engine formed of a stacked plurality of ceramic matrix composite (CMC) lamellae (12) supported by a metal support structure (20). Individual lamellae are supported directly by the support structure via cooperating interlock features (30, 32) formed on the lamella and on the support structure respectively. Mating load-transferring surfaces (34, 36) of the interlock features are disposed in a plane (44) oblique to local axes of thermal growth (38, 40) in order to accommodate differential thermal expansion there between with delta alpha zero expansion (DAZE). Reinforcing fibers (62) within the CMC material may be oriented in a direction optimized to resist forces being transferred through the interlock features. Individual lamellae may all have the same structure or different interlock feature shapes and/or locations may be used in different groups of the lamellae. Applications for this invention include an airfoil assembly (10) and a ring segment assembly (82).