The bank lending channel is heterogeneous across firms. Using matched bank-firm credit data, we develop a framework that  estimates the effects of firm-demand and bank-supply credit shocks, allowing for interactions between bank and firm unobserved factors. Bank shocks can have heterogeneous effects across firm types, where firm type is unobserved for the econometrician. We decompose credit growth dynamics into time-varying firm and bank-firm type interaction effects. We uncover significant heterogeneity in the bank lending channel: i) The effect of bank shocks varies considerably across the identified firm types, ii) During the Great Recession, more exposed banks severely contracted their loan supply to some firms but shielded others, iii) We uncover a bank-firm matching channel: the transmission of shocks crucially depends on the bank-firm network, with credit growth dropping by up to 20% in a counterfactual randomly matched network, iii) Accounting for interactions helps to more precisely estimate the impact of bank shocks on firm real outcomes.