The present work focuses on the interfacial mechanical behaviour of a model composite consisting of a solid droplet on a fibre, generally referred to as the microbond test. The interfacial adhesion is derived from the modelling of stress transfer in the microbond geometry including process-induced internal stresses, following two alternative approaches, namely the numerical discretisation of the droplet profile, and the equivalent cylinder analytical solution. This is in contrast to previous approaches, which mainly consider approximate geometry of the droplet. The numerical derivation provides comprehensive stress field data, whereas the equivalent cylinder approach is less accurate. However, these two approaches are shown to be equivalent as they result in the determination of the same interfacial shear strength. Numerical results clearly demonstrate that the maximum shear strength is located at the inflection point of the droplet profile. This provides an insight into the commonly observed remaining cone of resin on the fibre after debonding. It is further shown that the shear strength obtained by this method is independent of the location of the applied force, provided that the load is applied between the droplet end and its profile inflection point. The model is generalised to the case of a symmetric loading and therefore includes internal stresses. It is then used to predict experimental interfacial shear strength versus droplet length for epoxy/glass, epoxy/Kevlar and epoxy/carbon systems at different levels of internal stresses and contact angle values.