In this article we present and estimate a synthesis of previous equilibrium search models, allowing for continuous distributions of workers' opportunity costs of employment as well as firms' productivities. The model allows for on-the-job search, and we assume that job offer arrival rates for workers are independent of their labor-market state. We derive the theoretical implications of these assumptions, we provide simulations, and we develop a semiparametric estimation procedure that we apply to a dataset of individual labor-market histories.