I study the effects of large scale asset purchases in the mortgage market (QE) on aggregate consumption in a continuous-time heterogeneous agent New Keynesian model with lumpy housing and frictional financial intermediation. I find a salient house price channel of QE. In the presence of binding leverage constraints of intermediaries, QE is relevant through decreasing the borrowing spread. Since housing adjustment is lumpy, this lower spread substantially increases housing demand and house prices through accelerating the adjustment threshold. With heterogeneous agents and borrowing constraints, these higher house prices transmit to aggregate consumption through wealth, collateral, and general equilibrium effects.