The complex nature of real-world problems calls for heterogeneity in both machine learning (ML) models and hardware systems. The heterogeneity in ML models comes from multi-sensor perceiving and multi-task learning, i.e., multi-modality multi-task (MMMT), resulting in diverse deep neural network (DNN) layers and computation patterns. The heterogeneity in systems comes from diverse processing components, as it becomes the prevailing method to integrate multiple dedicated accelerators into one system. Therefore, a new problem emerges: heterogeneous model to heterogeneous system mapping (H2H). While previous mapping algorithms mostly focus on efficient computations, in this work, we argue that it is indispensable to consider computation and communication simultaneously for better system efficiency. We propose a novel H2H mapping algorithm with both computation and communication awareness; by slightly trading computation for communication, the system overall latency and energy consumption can be largely reduced. The superior performance of our work is evaluated based on MAESTRO modeling, demonstrating 15%-74% latency reduction and 23%-64% energy reduction compared with existing computation-prioritized mapping algorithms.