Extrusion-based additive manufacturing of cementitious material is a promising technology for the future of construction. Nevertheless, new solutions need to be proposed to provide either ductility or even reinforcement in areas in tension. Using fibres to reinforce the structure made by extrusion seems to be promising and needs to be fully understood at different scales. Moreover, the efficiency of reinforcement depends mainly on the interfacial properties between matrix and fibres. Decohesion between matrix and fibre is studied at two different scales. A mesoscopic analytical mechanical model of a so-called tension stiffening test has been proposed to quantify resistance and friction along the interface from the force-elongation curve. Secondly, the same experimental test is performed inside the microtomography setup of the Anatomix beamline of Synchrotron Soleil permitting to identify the microscopic nature, shape and the evolution of decohesion between matrix and fibres for different loading. Different types of fibres are compared and different damaging mechanisms are observed.