Deep neural networks (DNNs) are rapidly evolving from streamlined single-modality single-task (SMST) to multimodality multitask (MMMT) with large variations for different layers and complex data dependencies among layers. To support such models, hardware systems also evolved to be heterogeneous. The heterogeneous system comes from the prevailing trend to integrate diverse accelerators into the system for lower latency. FPGAs have high-computation density and communication bandwidth and are configurable to be deployed with different designs of accelerators, which are widely used for various machine-learning applications. However, scaling from SMST to MMMT on heterogeneous FPGAs is challenging since MMMT has much larger layer variations, a massive number of layers, and complex data dependency among different backbones. Previous mapping algorithms are either inefficient or over-simplified which makes them impractical in general scenarios. In this work, we propose CHEF to enable efficient implementation of MMMT models in realistic heterogeneous FPGA clusters, i.e., deploying heterogeneous accelerators on heterogeneous FPGAs (A2F) and mapping the heterogeneous DNNs on the deployed heterogeneous accelerators (M2A). We propose CHEF-A2F, a two-stage accelerators-to-FPGAs deployment approach to co-optimize hardware deployment and accelerator mapping. In addition, we propose CHEF-M2A, which can support general and practical cases compared to previous mapping algorithms. To the best of our knowledge, this is the first attempt to implement MMMT models in real heterogeneous FPGA clusters. Experimental results show that the latency obtained with CHEF is near-optimal while the search time is 10 $000\times$ less than exhaustively searching the optimal solution.