We build a New Keynesian business-cycle model with rich household heterogeneity. A central feature is that matching frictions render labor-market risk countercyclical and endogenous to monetary policy. Our main result is that a majority of households prefer substantial stabilization of unemployment even if this means deviations from price stability. A monetary policy focused on unemployment stabilization helps "Main Street" by providing consumption insurance. It hurts "Wall Street" by reducing precautionary saving and, thus, asset prices. On the aggregate level, household heterogeneity changes the transmission of monetary policy to consumption, but hardly to GDP. Central to this result is allowing for self-insurance and aggregate investment.