Six non-conventional in situ shear tests were carried out at the Santa Barbara disused open-pit mine (Italy) to investigate the strength properties of the Shale–Limestone Chaotic Complex bimrock. The SLCC is characterised by a dark-grey clayey matrix containing calcareous rock fragments of various sizes. A non-conventional in situ shear test apparatus has been developed for the purpose of the present research: the testing procedure ensures that the failure surface inside the specimen is free to develop in a tortuous way along block/matrix contacts, thus allowing for the evaluation of the bimrock strength parameters by taking into account the influence of the blocks and to overcome the size limitation of laboratory specimens. The operative strength parameters were correlated to the volumetric block content (VBC) inside the tested specimens, evaluated by means of in situ large-sized sieving tests. The data show a good linear positive correlation between the VBC and the bimrock friction angle, while cohesion seems to be strongly affected by a critical VBC threshold (20–25%). Moreover, the bimrock strength parameters show an overall larger friction angle and lower cohesion compared to those of the SLCC clayey matrix, in agreement with the common bimrock mechanical behaviour.