This paper analyzes the persistence and overlap of relationships between banks in a multiplex decomposition of the exposures network. Our analysis may be useful for researchers designing stress tests or models in which the behavior of banks is modeled explicitly. This has not been looked at previously, considering the time period involved and the different types of exposures and interactions used. We show that trading relationships overlap for some pairs of banks, and link persistence is higher in the secured than the unsecured market. Moreover, link persistence in the securities cross-holding network is much higher than in other funding networks, and overlap with the other segments of activity is low, despite being persistent over time. Additionally, unsecured loans received by large banks have the shortest waiting times (that is, for a given borrower and a given lender, the number of days elapsed before a new loan is observed) regardless of counterparty size, which suggests quicker access to liquidity. Large banks lend (unsecured) with shorter waiting times to medium-sized banks than to small banks; this is not the case when they lend in the secured layer of the network. Small banks have quicker access to liquidity in the secured lending layer when borrowing from medium-sized banks.