The recent development of high-altitude platforms (HAPs) has attracted increasing attention since they can serve as a promising communication method to assist satellite-terrestrial networks. In this paper, we consider an integrated three-layer satellite-HAP-terrestrial network where the HAP support dual-band connectivity. Specifically, the HAP can not only communicate with terrestrial users over C-band directly, but also provide backhaul services to terrestrial user terminals over Ka-band. We formulate a sum-rate maximization problem and then propose a fractional programming based algorithm to solve the problem by optimizing the bandwidth and power allocation iteratively. The closed-form optimal solutions for bandwidth allocation and power allocation in each iteration are also derived. Simulation results show the capacity enhancement brought by the dual-band connectivity of the HAP. The influence of the power of the HAP and the power of the satellite is also discussed.