In situ tensile tests in a scanning electron microscope (SEM) have been conducted on a 8-layer 5-harness satin carbon fibre and epoxy matrix composite to observe the first stages of damage at the scale of fibres and matrix. A speckle pattern based on a suspension of alumina particles was applied onto the surface of the specimen to facilitate the use of digital image correlation (DIC). Local and finite element (FE) DIC are compared on pictures acquired during the tensile tests, with and without a speckle pattern. FE DIC with mechanical regularization was found to be the only approach able to measure displacement fields at a fine enough resolution in both cases. This method, initially created for homogeneous materials, was then adapted to heterogeneous materials. First, a microstructure consistent mesh was created and used for correlation purposes. Second, the difference between the mechanical properties of the constituents is taken into account in the mechanical regularization. Last, the accuracy of the method is analysed. The adaptation presented herein was proved to be able to measure displacement fields in the matrix between fibres with an error of 10 nm (a fifth of a pixel) and to detect the initiation of the first damage mechanisms by means of the mechanical residuals.