Load-bearing tissues are composite materials that depend strongly on anisotropic fibre arrangement to maximise performance. One such tissue is the heart valve, with orthogonally arranged fibrosa and ventricularis layers. Their function is to maintain mechanical stress while being resilient. It is postulated that while one layer bears the applied stress, the orthogonal layer helps to regenerate the microstructure when the load is released. The present paper describes changes in the microstructure of a block copolymer with cylindrical morphology, having a bio-inspired microstructure of anisotropic orthogonally oriented layers, under uniaxial strain. To allow structural observations during fast deformation, equivalent to the real heart valve operation, we used a synchrotron X-ray source and recorded 2D SAXS patterns in only 1 ms per frame. The deformation behaviour of the composite microstructure has been reported for two arrangements of the cylinders in skin and core layers. The behaviour is very different to that observed either for uniaxially oriented or isotropic samples. Deformation is far from being affine. Cylinders aligned in the direction of stretch show fragmentation, but complete recovery of the spacing between cylinders on removal of the load. Those oriented perpendicular to the direction of stretch incline at an angle of approximately 25° to their original direction during load.