Joint communication and sensing (JCAS) has been recognized as a promising technology in the sixth generation (6G) communication. A realistic channel model is a prerequisite for designing JCAS systems. Most existing channel models independently generate the communication and sensing channels under the same framework. However, due to the multiplexing of hardware resources (e.g., antennas) and the same environment, signals enabled for communication and sensing may experience some 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 jointly reconstructed for both channels. In this paper, we first conduct communication and sensing channel measurements for an indoor scenario at 28 GHz. The power-angular-delay profiles (PADPs) of multipath components (MPCs) are obtained, and the shared scatterers by communication and sensing channels are intuitively observed. Then, a stochastic JCAS channel model is proposed to capture the sharing feature, where shared and non-shared clusters by the two channels are defined and superimposed. To extract those clusters from measured JCAS channels, a KPowerMeans-based joint clustering algorithm (KPM-JCA) is novelly introduced. Finally, stochastic channel characteristics are analyzed, and the practicality and controllability of the proposed model are validated based on the measurements and empirical simulations. The proposed model can realistically capture the sharing feature of JCAS channels, which is valuable for the design and deployment of JCAS systems.