This paper assesses the resilience of Eurozone banks' equity and liquidity against large shocks to financial markets. Our analysis refers to 35 banks in the Eurozone from 2005 to 2015. We adopt a new type of model that combines copulas and non-linear factorial structures in order to treat the case of large sets of multiclass assets exposed to extreme risks. Our contribution is fourfold. First, we employ a model that accounts for teh senistivity of the Asset as well Liability sides. Second, we measure the impact of different sources of shocks ( stock, bond, sovereign bond markets,...) not only on banks' solvency but also on their liquidity positions, third, we take into account second round and spillover effects between different financial markets and countries, illustrating potential contagion cases. Fourth, we assess the role of diversification in improving banks' resilience by examining the particular situation where stock and bond returns become positively dependent, as recently observed. Our main findings are: taking into account interdependency between items of the balance sheets indeed matters; liquidity shortfalls are substantial compared to capital ones and banks' fragility remains still high in 2015. Contagion risks remain high. Finally, losing diversification opportunities when stock and bond returns become slightly positively related, increase capital and mainly liquidity shortfalls with an increase around 20\% for some Italian banks in the atter case and above 80\% for Greek banks and around 70\% for a French bank, in the former case.