This paper presents a modeling and analysis framework for downlink communications in a heterogeneous Low Earth Orbit (LEO) satellite network. The study investigates the coexistence of multiple LEO satellite constellations sharing the same spectrum resources, focusing on the impact of interference and the performance of two access technologies: closed access and open access. The network is modeled using a Cox point process, which allows for the representation of satellites on various orbits. The analysis derives the coverage probability for both access scenarios, showing that open access outperforms closed access in terms of coverage. The framework considers the geometric features of the network, including different satellite altitudes, orbit structures, and constellation types. The study also evaluates the performance metrics of the network, including the no-satellite probability and coverage probability, under various conditions. The results demonstrate that open access significantly improves the coverage of all user percentiles, making it a more effective solution for future heterogeneous LEO satellite networks. The analysis is supported by simulations and theoretical derivations, providing a tractable method for designing, evaluating, and optimizing such networks.This paper presents a modeling and analysis framework for downlink communications in a heterogeneous Low Earth Orbit (LEO) satellite network. The study investigates the coexistence of multiple LEO satellite constellations sharing the same spectrum resources, focusing on the impact of interference and the performance of two access technologies: closed access and open access. The network is modeled using a Cox point process, which allows for the representation of satellites on various orbits. The analysis derives the coverage probability for both access scenarios, showing that open access outperforms closed access in terms of coverage. The framework considers the geometric features of the network, including different satellite altitudes, orbit structures, and constellation types. The study also evaluates the performance metrics of the network, including the no-satellite probability and coverage probability, under various conditions. The results demonstrate that open access significantly improves the coverage of all user percentiles, making it a more effective solution for future heterogeneous LEO satellite networks. The analysis is supported by simulations and theoretical derivations, providing a tractable method for designing, evaluating, and optimizing such networks.