In this paper, we investigate the optimal power and time allocation for a wireless relay network, called BCFR (Broadcasting Channel with Fixed Relay), where the relay node is limited by the half-duplex operation. Introducing a relay in two-node broadcasting channel for a node which has a link of bad quality or requires higher transmission rate enlarges the rate region with well-designed power and time allocation. Also, BCFR is a common component of many relay networks, in which either orthogonal or non-orthogonal transmission can be adopted at the information source node. In particular, for the non-orthogonal transmission, the layered transmission with superposition coding is applied at the source node. By deriving the optimal power and time-fraction allocation at each node of BCFR, we show that the non-orthogonal structure enhances the capacity region and achieves higher log-sum capacity than the orthogonal transmission.