This article develops a novel approach and algorithmic tools for the modeling and survivability analysis of networks with heterogeneous nodes, and examines their application to space-based networks. Space-based networks (SBNs) allow the sharing of spacecraft on-orbit resources, such as data storage, processing, and downlink. Each spacecraft in the network can have different subsystem composition and functionality, thus resulting in node heterogeneity. Most traditional survivability analyses of networks assume node homogeneity and as a result, are not suited for the analysis of SBNs. This work proposes that heterogeneous networks can be modeled as interdependent multi-layer networks, which enables their survivability analysis. The multi-layer aspect captures the breakdown of the network according to common functionalities across the different nodes, and it allows the emergence of homogeneous sub-networks, while the interdependency aspect constrains the network to capture the physical characteristics of each node. Definitions of primitives of failure propagation are devised. Formal characterization of interdependent multi-layer networks, as well as algorithmic tools for the analysis of failure propagation across the network are developed and illustrated with space applications. The SBN applications considered consist of several networked spacecraft that can tap into each other's Command and Data Handling subsystem, in case of failure of its own, including the Telemetry, Tracking and Command, the Control Processor, and the Data Handling sub-subsystems. Various design insights are derived and discussed, and the capability to perform trade-space analysis with the proposed approach for various network characteristics is indicated. The select results here shown quantify the incremental survivability gains (with respect to a particular class of threats) of the SBN over the traditional monolith spacecraft. Failure of the connectivity between nodes is also examined, and the results highlight the importance of the reliability of the wireless links between spacecraft (nodes) to enable any survivability improvements for space-based networks.