Integrated sensing and communication enables sensing capability for wireless networks. However, the interference management and resource allocation between sensing and communication have not been fully studied. In this paper, we consider the design of perceptive mobile networks (PMNs) by adding sensing capability to current cellular networks. To avoid the full-duplex operation and reduce interference, we propose the PMN with distributed target monitoring terminals (TMTs) where passive TMTs are deployed over wireless networks to locate the sensing target (ST). We then jointly optimize the transmit and receive beamformers towards the communication user terminals (UEs) and the ST by alternating-optimization (AO) and prove its convergence. To reduce computation complexity and obtain physical insights, we further investigate the use of linear transceivers, including zero forcing and beam synthesis (B-syn), and show that B-syn can achieve comparable sensing performance as AO especially when the communication requirement is high. Some interesting physical insights are also revealed. For example, instead of forming a dedicated sensing signal, it is more efficient to jointly design the communication signals for different UEs such that they ``collaboratively leak" energy to the ST. Furthermore, the amount of energy leakage from one UE to the ST depends on their relative locations.