In this research, the Poisson's ratio of three different types of almost isotropic interpenetrating composites are designed to be either positive, or negative, or zero. As they are strengthened by a self-connected fibre-network and do not contain any pore in their structure, they all are stiffer than the conventional particle composites. In addition, structural hierarchy is also demonstrated to be able to significantly enhance the auxetic behaviour for the three types of interpenetrating composites. Thus, these composites could be used not only as functional materials, but also as structural materials in engineering applications.