Due to the limitations of current spectral imaging equipment in acquiring high-resolution hyperspectral images (HR-HSIs), a common approach is to fuse low-resolution hyperspectral images (LR-HSIs) with high-resolution multispectral images (HR-MSIs). However, most existing methods have not fully taken into account the correlation and discrepancy in modality between hyperspectral images (HSIs) and multispectral images (MSIs). To address this limitation, we propose an innovative spectral modality-aware interactive fusion network (SMIF-NET) for comprehensive extraction of spectral information and seamless feature fusion. First, we introduce the spectral modality-aware transformer (SMAT) with a dual-attention mechanism to compute spectral self-similarity and cross-spectral correlation. Second, we apply the interactive spatial-spectral feature fusion (IS2F2) to fuse the acquired high-level spectral and spatial features. This fusion technique combines spatial-wise and channel-wise squeeze and excitation to achieve seamless integration of spatial-spectral information. Finally, the extensive experiments on three datasets demonstrate the superior performance of SMIF-NET in both visual and quantitative assessments compared to eight state-of-the-art (SOTA) fusion-based methods.