In this work, we aim to effectively characterize the performance of cooperative integrated sensing and communication (ISAC) networks and to reveal how performance metrics relate to network parameters. To this end, we introduce a generalized stochastic geometry framework to model the cooperative ISAC networks, which approximates the spatial randomness of the network deployment. Based on this framework, we derive analytical expressions for key performance metrics in both communication and sensing domains, with a particular focus on communication coverage probability and radar information rate. The analytical expressions derived explicitly highlight how performance metrics depend on network parameters, thereby offering valuable insights into the deployment and design of cooperative ISAC networks. In the end, we validate the theoretical performance analysis through Monte Carlo simulation results. Our results demonstrate that increasing the number of cooperative base stations (BSs) significantly improves both metrics, while increasing the BS deployment density has a limited impact on communication coverage probability but substantially enhances the radar information rate. Additionally, increasing the number of transmit antennas is effective when the total number of transmit antennas is relatively small. The incremental performance gain reduces with the increase of the number of transmit antennas, suggesting that indiscriminately increasing antennas is not an efficient strategy to improve the performance of the system in cooperative ISAC networks.