A multi-layer ceramic matrix composite structure (40) having a plurality of fiber-reinforced cooling passages (42) formed therein. The cooling passages are formed by the removal of a fugitive material (24). The fugitive material is part of a wrapped fugitive material structure (28) containing a layer of reinforcing ceramic fibers (26) that is used to lay-up the multi-layer structure. An intermediate layer of ceramic fabric 56 may be placed alternately over and under the wrapped fugitive material structure to separate the cooling passages into alternating upper (54) and lower (52) cooling passages. The transversely oriented fibers surrounding the cooling passages serve to increase the interlaminar strength of the structure when compared to prior art designs. An airfoil member (112) incorporating such reinforced integral cooling passages (120) is provided.