If unaligned multimodal medical images can be simultaneously aligned and fused using a single-stage approach within a unified processing framework, it will not only achieve mutual promotion of dual tasks but also help reduce the complexity of the model. However, the design of this model faces the challenge of incompatible requirements for feature fusion and alignment. To address this challenge, this paper proposes an unaligned medical image fusion method called Bidirectional Stepwise Feature Alignment and Fusion (BSFA-F) strategy. To reduce the negative impact of modality differences on cross-modal feature matching, we incorporate the Modal Discrepancy-Free Feature Representation (MDF-FR) method into BSFA-F. MDF-FR utilizes a Modality Feature Representation Head (MFRH) to integrate the global information of the input image. By injecting the information contained in MFRH of the current image into other modality images, it effectively reduces the impact of modality differences on feature alignment while preserving the complementary information carried by different images. In terms of feature alignment, BSFA-F employs a bidirectional stepwise alignment deformation field prediction strategy based on the path independence of vector displacement between two points. This strategy solves the problem of large spans and inaccurate deformation field prediction in single-step alignment. Finally, Multi-Modal Feature Fusion block achieves the fusion of aligned features. The experimental results across multiple datasets demonstrate the effectiveness of our method.