In the vehicle industry it is common to find structures that are required to carry mechanical loads while not experiencing large vibrations when subjected to dynamic loads. An important design tool to achieve this is topology optimization. In the presented work, a mixed-integer programming extension to the established Topology Optimization of Binary Structures (TOBS) method is used to concurrently optimize core topology and face sheet thickness of a sandwich beam subjected to static and time-harmonic loading. The proposed method allows for optimization of the core topology without the face sheet thickness being known a priori. The static and dynamic compliance are used as measures of the response to static and time-harmonic loading and the goal of the optimization is to minimize the mass of the beam subjected to constraints on the compliances. The beam is optimized for different excitation frequencies. The results show that the method is able to find solutions with low mass that satisfy both static and dynamic constraints.