A flexible probabilistic approach for the constructing of realistic topologies of interbank networks is presented. This constitutes a challenging task, since information on bilateral inter-banking activities is classified confidential and the number of banks in most European countries is substantial. Firstly, we analyze what information on European inter-banking liabilities is publicly available. Second, we present an approach for the reconstruction of network topologies satisfying known characteristics through an exponential random graph model (ERGM), which incorporates the available information as side conditions. Third, we conduct a case study calibrating the model to the Italian and the German interbank market. Samples of both models are then analyzed with respect to different network statistics. The relevance of the presented results stems from the urgent need of having realistic instances of possible adjacency matrices as input in technical studies on the stability of inter-banking networks. Various such studies exist, however, most of them rely on toy models for the analyzed adjacency matrices.