This paper aims to disentangle the impact of multiple transmission channels in interbank connectedness. We use the identification properties of a structural vector autoregression with a multivariate GARCH-in-mean structure (SVAR-MGARCH-M) to model the dynamics in equity returns of the Eurozone systemically important financial institutions (SIFIs). We can identify the impacts of multiple transmission channels such as asset communality, interbank deposits, and information contagion. Asset communality is both a factor in the transmission of shocks and a means of diversification: heightened connectedness results in an increase in shock spillovers, which are countered by risk sharing benefits. We show that connectedness increased during the financial crisis with a major role for common exposures. Institutions move from being a net recipient to a net transmitter of shocks when the asset communality channel is taken into account, suggesting that we need to evaluate the systemic importance of an institution using all transmission components.