Integrating multimodal data of pathological image and gene expression for cancer survival analysis can achieve better results than using a single modality. However, existing multimodal learning methods ignore fine-grained interactions between both modalities, especially the interactions between biological pathways and pathological image patches. In this article, we propose a novel Pathway-Aware Multimodal Transformer (PAMT) framework for interpretable cancer survival analysis. Specifically, the PAMT learns fine-grained modality interaction through three stages: (1) In the intra-modal pathway-pathway / patch-patch interaction stage, we use the Transformer model to perform intra-modal information interaction; (2) In the inter-modal pathway-patch alignment stage, we introduce a novel label-free contrastive loss to aligns semantic information between different modalities so that the features of the two modalities are mapped to the same semantic space; and (3) In the inter-modal pathway-patch fusion stage, to model the medical prior knowledge of "genotype determines phenotype", we propose a pathway-to-patch cross fusion module to perform inter-modal information interaction under the guidance of pathway prior. In addition, the inter-modal cross fusion module of PAMT endows good interpretability, helping a pathologist to screen which pathway plays a key role, to locate where on whole slide image (WSI) are affected by the pathway, and to mine prognosis-relevant pathology image patterns. Experimental results based on three datasets of bladder urothelial carcinoma, lung squamous cell carcinoma, and lung adenocarcinoma demonstrate that the proposed framework significantly outperforms the state-of-the-art methods.