Integrated sensing and communication (ISAC) is a cornerstone technology for 6G networks, offering unified support for high-rate communication and high-accuracy sensing. While existing literature extensively covers link-level designs, the transition toward large-scale deployment necessitates a fundamental understanding of network-level performance. This paper investigates a network ISAC model where a source node communicates with a destination via a relay network, while intermediate nodes concurrently perform cooperative sensing over specific spatial regions. We formulate a novel optimization framework that captures the interplay between multi-node routing and sensing coverage. For a one-dimensional path network, we provide an analytical characterization of the complete sensing-throughput region. Extending this to general network topologies, we establish that the sensing-throughput Pareto boundary is piecewise linear and provide physical interpretations for each segment. Our results reveal the fundamental trade-offs between sensing coverage and communication routing, offering key insights for the design of future 6G heterogeneous networks.