In this paper, we study the co-design of full-duplex (FD) radio with joint communication and radar sensing (JCAS) techniques in millimeter-wave (mmWave) heterogeneous networks (HetNets). Spectral co-existence of radar and communication systems causes mutual interference between the two systems, compromising both the data exchange and sensing capabilities. Focusing on the detection performance, we propose a cooperative detection technique, which exploits the sensing information from multiple base stations (BSs), aiming at enhancing the probability of successfully detecting an object. Three combining rules are considered, namely the \textit{OR}, the \textit{Majority} and the \textit{AND} rule. In real-world network scenarios, the locations of the BSs are spatially correlated, exhibiting a repulsive behavior. Therefore, we model the spatial distribution of the BSs as a $β$-Ginibre point process ($β$-GPP), which can characterize the repulsion among the BSs. By using stochastic geometry tools, analytical expressions for the detection performance of $β$-GPP-based FD-JCAS systems are expressed for each of the considered combining rule. Furthermore, by considering temporal interference correlation, we evaluate the probability of successfully detecting an object over two different time slots. Our results demonstrate that our proposed technique can significantly improve the detection performance when compared to the conventional non-cooperative technique.