The Chamaeleon molecular cloud complex is one of the nearest star-forming sites encompassing three molecular clouds with a different star-formation history, from quiescent (Cha III) to actively forming stars (Cha II), and reaching the end of star-formation (Cha I). To charactize its large-scale structure, we derived column density and temperature maps using PACS and SPIRE observations from the Herschel Gould Belt Survey, and applied several tools, such as filament tracing, power-spectra, \Delta-variance, and probability distribution functions of column density (PDFs), to derive physical properties. The column density maps reveal a different morphological appearance for the three clouds, with a ridge-like structure for Cha I, a clump-dominated regime for Cha II, and an intricate filamentary network for Cha III. The filament width is measured to be around 0.12\pm0.04 pc in the three clouds, and the filaments found to be gravitationally unstable in Cha I and II, but mostly subcritical in Cha III. Faint filaments (striations) are prominent in Cha I showing a preferred alignment with the large-scale magnetic field. The PDFs of all regions show a lognormal distribution at low column densities. For higher densities, the PDF of Cha I shows a turnover indicative of an extended higher density component, culminating with a power-law tail. Cha II shows a power-law tail with a slope characteristic of gravity. The PDF of Cha III can be best fit by a single lognormal. The turbulence properties of the three regions are found to be similar, pointing towards a scenario where the clouds are impacted by large-scale processes. The magnetic field could possibly play an important role for the star-formation efficiency in the Chamaeleon clouds if proven that it can effectively channel material on Cha I, and possibly Cha II, but probably less efficiently on the quiescent Cha III cloud.< Réduire