HDD is a duplexing scheme that combines TDD and FDD, taking the advantages of both systems. In this paper a novel overlaid HDD system concept is proposed. The proposed overlaid HDD system uses both TDD and FDD in both regions via two paired frequency bands. Our design objective is to propose an adequate frame structure for the overlaid HDD system with fixed relay stations to enhance the system throughput, especially for the outer region. The frequency reuse factors for the inner and the outer region are set differently to overcome the interference from other cells. It is shown that in the proposed overlaid HDD system, the throughput of the outer region is increased by 58% in the UL and 20% in the DL at 5% throughput loss of the inner region both in the UL and DL compared to that of the overlaid HDD system without relay stations. Also, the proposed overlaid system has 9% gain in the DL compared to the singleband system with relay stations.