The median U-turn intersection is a potential method for relieving traffic congestion at intersections. Median U-turn intersections can be classified into six types, according to the prohibited traffic movements. Although much is known about the technology of the median U-turn, efforts have focused on its geometric design, safety analysis, and evaluation. In this paper, a lane-based optimization model is proposed for the integrated design of median U-turn intersection types, lane markings, distances between the median crossovers and the main intersection, and signal timings. The capacity maximization problem is considered, and a set of constraints is determined that ensures the feasibility and safety of the optimization results. The optimization is formulated as a multi-objective mixed-integer nonlinear programming problem. It is solved by transformation to a series of mixed-integer linear programming models. The latter can be solved by the standard branch-and-bound technique. Extensive numerical analysis and a case study have shown the effectiveness of the proposed method. In addition, the method can assist transportation professionals in the proper selection of U-turn types and in the design of intersections with median U-turns.