Thermostructural composite structure having a compositional gradient, formed from a porous core (5) made of a refractory having a pore volume content of greater than or equal to 80%. The core (5) lies between two intermediate layers (6a, 6b) comprising the carbon fiber reinforcement, densified by a matrix composed of the carbon phase and of a ceramic phase, and a refractory solid filler. Two monolithic ceramic shells (7a, 7b) cover the intermediate layers in order to give stiffness to the entire structure.