We propose a distress measure for national banking systems that incorporates not only banks’ CDS spreads, but also how they interact with the rest of the global financial system via multiple linkage types. The measure is based on a tensor decomposition method that extracts an adjacency matrix from a multi-layer network, measured using banks’ foreign exposures obtained from the BIS international banking statistics. Based on this adjacency matrix, we develop a new network centrality measure that can be interpreted in terms of a banking system's credit risk or funding risk.