Co-continuous network polymers (CNPs) as the new polymer composites are fabricated by filling the continuous pores of an epoxy monolith with a high glass transition temperature (Tg) using another kind of network polymer with a low Tg. In this study, we prepared sheet-like and cylindrical CNPs using thiol–ene thermosets as the second component with a low Tg. A thiol–ene reaction is suitable for the preparation of thermosets with a controlled network structure. Here, various thiols and acrylates including the different numbers of functional groups and/or oligo(ethylene oxide) spacers with different lengths are used for the fabrication of the second thermosetting component. We investigated the tensile and compression mechanical properties of the produced CNPs. Dynamic mechanical analysis (DMA) of the thiol–ene bulk thermosets (BTs) as the second component was also carried out in order to clarify the influence of the Tg and the crosslinking density on the mechanical and physical properties of the CNPs. The results of the mechanical tests were discussed on the functionality of the used acrylate and thiol compounds. In conclusion, we have revealed that the properties of CNPs are not only dependent on the crosslinking density, but also significantly affected by the detailed network structure of the second component.