The financial distress of a banking system can be measured by the risk premia implied by the corresponding set of CDS spreads which, in efficient markets, can incorporate all information relevant to correctly measure solvency risk and, therefore, a correct predictor of CDS spreads can be a very important early warning measure of a crisis. We claim that a good predictor should take contagion between banking systems into account. To achieve this aim, we propose a distress measure for banking systems that incorporates not only their CDS spreads, but also how they interact with the rest of the global financial system via multiple linkage types. The measure employs a tensor decomposition method to extract one adjacency matrix from a multi-layer network, based on banks' foreign exposures obtained from the BIS international banking statistics. It then develops a new network centrality measure that can be probabilistically interpreted in terms of credit risk or funding risk of a banking system,taking multiple types of foreign exposures into account.