Hand gesture recognition (HGR) based on surface electromyogram (sEMG) and Accelerometer (ACC) signals is increasingly attractive where fusion strategies are crucial for performance and remain challenging. Currently, neural network-based fusion methods have gained superior performance. Nevertheless, these methods typically fuse sEMG and ACC either in the early or late stages, overlooking the integration of entire cross-modal hierarchical information within each individual hidden layer, thus inducing inefficient inter-modal fusion. To this end, we propose a novel Alignment-Enhanced Interactive Fusion (AiFusion) model, which achieves effective fusion via a progressive hierarchical fusion strategy. Notably, AiFusion can flexibly perform both complete and incomplete multimodal HGR. Specifically, AiFusion contains two unimodal branches and a cascaded transformer-based multimodal fusion branch. The fusion branch is first designed to adequately characterize modality-interactive knowledge by adaptively capturing inter-modal similarity and fusing hierarchical features from all branches layer by layer. Then, the modality-interactive knowledge is aligned with that of unimodality using cross-modal supervised contrastive learning and online distillation from embedding and probability spaces respectively. These alignments further promote fusion quality and refine modality-specific representations. Finally, the recognition outcomes are set to be determined by available modalities, thus contributing to handling the incomplete multimodal HGR problem, which is frequently encountered in real-world scenarios. Experimental results on five public datasets demonstrate that AiFusion outperforms most state-of-the-art benchmarks in complete multimodal HGR. Impressively, it also surpasses the unimodal baselines in the challenging incomplete multimodal HGR. The proposed AiFusion provides a promising solution to realize effective and robust multimodal HGR-based interfaces.