This paper analyzes the distribution of lending and borrowing credit spreads in the European interbank market conditional on main features of banks such as their size, operating currency and nationality. This is done by means of nonparametric kernel estimation methods for the cross-sectional density of interbank funding rates over a large sample of European banks trading in the e-MID market. The analysis is repeated over consecutive non-overlapping periods in order to assess and compare the effect of the factors during crisis and non-crisis periods. We find evidence of important differences between the borrowing and lending segment of the interbank market that are augmented during crises periods. Our results strongly support the existence of a size effect in the borrowing market. Largest banks enjoy the highest lending rates and the lowest borrowing rates. The collapse of Lehman Brothers accentuates the differences in funding conditions. In both borrowing and lending segments, crises are corresponded by high volatilities in daily funding costs. Banks using the Euro currency and in countries not affected by sovereign debt crises are benefited by lower funding costs. Our nonparametric analysis of densities conditional on banks' nationality suggests that distress in the interbank market can serve as an early warning indicator of sovereign risk.