With the popularization of electric vehicles and the advancement in battery swapping technology, the number of battery swapping stations is increasing rapidly. In the meantime, a new type of station, integrated battery swapping and charging station (BSCS), has emerged, combining the functions of charging and battery swapping. In this paper, we study the design problem of the BSCSs, including determining the capacity allocation and a discount price. We employ a choice model to describe customer behavior and develop a novel queuing model for the BSCS. Furthermore, a recursive algorithm is provided to evaluate the system performance. In the numerical analysis, we discuss some basic cases and the effects of several key factors on the system.