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Future quantum networks will be hybrid structures, constructed from complex architectures of quantum repeaters interconnected by quantum channels that describe a variety of physical domains; predominantly optical-fiber and free-space links. In this hybrid setting, the interplay between the channel quality within network sub-structures must be carefully considered, and is pivotal for ensuring high-rate end-to-end quantum communication. In this work, we combine recent advances in the theory of point-to-point free-space channel capacities and end-to-end quantum network capacities in order to develop critical tools for the study of hybrid, free-space quantum networks. We present a general formalism for studying the capacities of arbitrary, hybrid quantum networks, before specifying to the regime of atmospheric and space-based quantum channels. We then introduce a class of modular quantum network architectures which offer a realistic and readily analysable framework for hybrid quantum networks. By considering a physically motivated, highly connected modular structure we are able to idealize network performance and derive channel conditions for which optimal performance is guaranteed. This allows us to reveal vital properties for which distance-independent rates are achieved, so that the end-to-end capacity has no dependence on the physical separation between users. Our analytical method elucidates key infrastructure demands for a future satellite-based global quantum internet, and for hybrid wired/wireless metropolitan quantum networks.