The recent surge of interest surrounding Multimodal Neural Networks (MM-NN) is attributed to their ability to effectively process and integrate multiscale information from diverse data sources. MM-NNs extract and fuse features from multiple modalities using adequate unimodal backbones and specific fusion networks. Although this helps strengthen the multimodal information representation, designing such networks is labor-intensive. It requires tuning the architectural parameters of the unimodal backbones, choosing the fusing point, and selecting the operations for fusion. Furthermore, multimodality AI is emerging as a cutting-edge option in Internet of Things (IoT) systems where inference latency and energy consumption are critical metrics in addition to accuracy. In this paper, we propose Harmonic-NAS, a framework for the joint optimization of unimodal backbones and multimodal fusion networks with hardware awareness on resource-constrained devices. Harmonic-NAS involves a two-tier optimization approach for the unimodal backbone architectures and fusion strategy and operators. By incorporating the hardware dimension into the optimization, evaluation results on various devices and multimodal datasets have demonstrated the superiority of Harmonic-NAS over state-of-the-art approaches achieving up to 10.9% accuracy improvement, 1.91x latency reduction, and 2.14x energy efficiency gain.