Existing learning-based methods effectively reconstruct HDR images from multi-exposure LDR inputs with extended dynamic range and improved detail, but they rely more on empirical design rather than theoretical foundation, which can impact their reliability. To address these limitations, we propose the cross-iterative Alignment and Fusion deep Unfolding Network (AFUNet), where HDR reconstruction is systematically decoupled into two interleaved subtasks -- alignment and fusion -- optimized through alternating refinement, achieving synergy between the two subtasks to enhance the overall performance. Our method formulates multi-exposure HDR reconstruction from a Maximum A Posteriori (MAP) estimation perspective, explicitly incorporating spatial correspondence priors across LDR images and naturally bridging the alignment and fusion subproblems through joint constraints. Building on the mathematical foundation, we reimagine traditional iterative optimization through unfolding -- transforming the conventional solution process into an end-to-end trainable AFUNet with carefully designed modules that work progressively. Specifically, each iteration of AFUNet incorporates an Alignment-Fusion Module (AFM) that alternates between a Spatial Alignment Module (SAM) for alignment and a Channel Fusion Module (CFM) for adaptive feature fusion, progressively bridging misaligned content and exposure discrepancies. Extensive qualitative and quantitative evaluations demonstrate AFUNet's superior performance, consistently surpassing state-of-the-art methods. Our code is available at: https://github.com/eezkni/AFUNet