Interferometric Hyperspectral Imaging (IHI) is a critical technique for large-scale remote sensing tasks due to its advantages in flux and spectral resolution. However, IHI is susceptible to complex errors arising from imaging steps, and its quality is limited by existing signal processing-based reconstruction algorithms. Two key challenges hinder performance enhancement: 1) the lack of training datasets. 2) the difficulty in eliminating IHI-specific degradation components through learning-based methods. To address these challenges, we propose a novel IHI reconstruction pipeline. First, based on imaging physics and radiometric calibration data, we establish a simplified yet accurate IHI degradation model and a parameter estimation method. This model enables the synthesis of realistic IHI training datasets from hyperspectral images (HSIs), bridging the gap between IHI reconstruction and deep learning. Second, we design the Interferometric Hyperspectral Reconstruction Unfolding Transformer (IHRUT), which achieves effective spectral correction and detail restoration through a stripe-pattern enhancement mechanism and a spatial-spectral transformer architecture. Experimental results demonstrate the superior performance and generalization capability of our method.