Microservice-based systems often suffer from reliability issues due to their intricate interactions and expanding scale. With the rapid growth of observability techniques, various methods have been proposed to achieve failure diagnosis, including root cause localization and failure type identification, by leveraging diverse monitoring data such as logs, metrics, or traces. However, traditional failure diagnosis methods that use single-modal data can hardly cover all failure scenarios due to the restricted information. Several failure diagnosis methods have been recently proposed to integrate multimodal data based on deep learning. These methods, however, tend to combine modalities indiscriminately and treat them equally in failure diagnosis, ignoring the relationship between specific modalities and different diagnostic tasks. This oversight hinders the effective utilization of the unique advantages offered by each modality. To address the limitation, we propose \textit{TVDiag}, a multimodal failure diagnosis framework for locating culprit microservice instances and identifying their failure types (e.g., Net-packets Corruption) in microservice-based systems. \textit{TVDiag} employs task-oriented learning to enhance the potential advantages of each modality and establishes cross-modal associations based on contrastive learning to extract view-invariant failure information. Furthermore, we develop a graph-level data augmentation strategy that randomly inactivates the observability of some normal microservice instances during training to mitigate the shortage of training data. Experimental results show that \textit{TVDiag} outperforms state-of-the-art methods in multimodal failure diagnosis, achieving at least a 55.94\% higher $HR@1$ accuracy and over a 4.08\% increase in F1-score across two datasets.