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Integrated Sensing And Communication (ISAC) has been recognized as a promising technology in the 6G communication. A realistic channel model is a prerequisite for designing ISAC systems. Most existing channel models independently generate the communication and sensing channels under the same framework. However, due to the multiplexing of hardware resources and the same environment, signals enabled for communication and sensing may experience shared propagation scatterers. This practical sharing feature necessities the joint generation of communication and sensing channels for realistic modeling, where the shared clusters (contributed by the shared scatterers) should be reconstructed.In this paper, we first conduct communication and sensing channel measurements for an indoor scenario at 28 GHz. The power-angular-delay profiles of multipath components are obtained, and the shared scatterers by communication and sensing channels are intuitively observed. Then, a stochastic ISAC channel model is proposed to capture the sharing feature, where shared and non-shared clusters by the two channels are dfined and superimposed. To extract those clusters from measured ISAC channels, a KPowerMeans-based joint clustering algorithm is novelly introduced. Finally, stochastic channel characteristics are analyzed, and empirical simulations validate that the channel Sharing Degree (SD) increases with more shared clusters. The proposed model can realistically capture the sharing feature of ISAC channels and is able to evaluate and simulate the channel SD values, which is valuable for the design and deployment of ISAC systems.