This paper estimates a structural model of unconventional monetary policy transmission through bank balance sheets using cross-sectional instruments for loan and deposit demand. We estimate the demand for banking at a branch-specific level from the response of a bank's quantities at one branch to interest rate changes caused by demand shocks at other branches. Depositors are considerably less sensitive to interest rates than corporate or mortgage borrowers. We use our demand estimates to infer a bank's marginal cost of borrowing and lending and apply a novel procedure to estimate how these costs depend on the composition of a bank's entire balance sheet. We use our estimated model for a counterfactual quantitative easing, in which a $4.76 trillion supply of bank reserves causes a 15 basis point increase in the yield on reserves. The increase in reserves crowds out bank lending by $555.9 billion, which implies that liquid reserves and illiquid loans are substitutes rather than complements for banks. We also find a modest $15.4 billion increase in bank deposits due to their inelastic demand.