Semantic communication has emerged as new paradigm shifts in 6G from the conventional syntax-oriented communications. Recently, the wireless broadcast technology has been introduced to support semantic communication system toward higher communication efficiency. Nevertheless, existing broadcast semantic communication systems target on general representation within one stage and fail to balance the inference accuracy among users. In this paper, the broadcast encoding process is decomposed into compression and fusion to improves communication efficiency with adaptation to tasks and channels.Particularly, we propose multiple task-channel-aware sub-encoders (TCE) and a channel-aware feature fusion sub-encoder (CFE) towards compression and fusion, respectively. In TCEs, multiple local-channel-aware attention blocks are employed to extract and compress task-relevant information for each user. In GFE, we introduce a global-channel-aware fine-tuning block to merge these compressed task-relevant signals into a compact broadcast signal. Notably, we retrieve the bottleneck in DeepBroadcast and leverage information bottleneck theory to further optimize the parameter tuning of TCEs and CFE.We substantiate our approach through experiments on a range of heterogeneous tasks across various channels with additive white Gaussian noise (AWGN) channel, Rayleigh fading channel, and Rician fading channel. Simulation results evidence that the proposed DeepBroadcast outperforms the state-of-the-art methods.