An insulated CMC structure (20A) formed of a CMC layer (22A), a thermal insulation layer (24A) applied to a front surface (30A) of the CMC layer (22A), and cooling channels (28A) formed along the interface (26A) between the CMC layer and the thermal insulation layer, thus directly cooling the thermally critical area of the interface. Embodiments include cooling channels in direct contact with both layers (FIG. 1); cooling channels in one layer and tangent to the other layer (FIGS. 4, 5 and 9); cooling channels in the CMC layer with an intervening wall (36D, 36E) that bulges into the thermal insulation layer for improved bonding thereof (FIGS. 6, 7); and cooling channels formed in ceramic tubes (38F of FIG. 8).