A ceramic matrix composite wall structure (20A) constructed of interlocking layers (22A, 24A) of woven material with integral cooling channels (28A, 32A). The CMC layer closest to the hot gas path (41) contains internal cooling tubes (26A, 30A) protruding into a ceramic insulating layer (40A). This construction provides a cooled CMC lamellate wall structure with an interlocking truss core.