Grazing-incidence X-ray reflectivity (GIXRR) is a widely used analysis method for thin films and multilayer structures. However, conventional so-called model-based approaches of structural reconstruction from GIXRR data lack flexibility when dealing with very thin structures (down to the nanometre scale), because a priori assumptions have to be made about the interface composition and structure. This makes it very difficult to extract reliable information about such structures. In this work, a custom free-form approach is presented, which solves this task without the need for a priori assumptions on layer or interface parameters. As a proof of principle, an optical constant profile reconstruction and GIXRR curve matching for simulated data are demonstrated. The developed approach is used to analyse the structures of multilayer LaN/B Bragg reflectors designed for the extreme UV range. The performed analysis allowed the difference in optical constant profiles of these structures produced with different processes to be revealed. The uncertainties of structural reconstruction are also discussed.