Precise identification of IDH mutation status in gliomas plays a vital role in directing tumor treatment Conventional methods often struggle to capture long-range dependencies efficiently or incur high computational costs when processing brain tumor MRI images. Recently, state-space models (SSMs), particularly Mamba deep learning models, have shown promise in long-sequence modeling with hardware efficiency. This paper introduces a multi-task learning framework, Bi-directional Mamba-U-Net Convolutional Integration Network (BMC-Net), which incorporates a hybrid CNN-Bi-directional Deep Interaction Augmented Mamba (CNN-BDIAM) encoder. This design integrates the capacity of CNNs for extracting local features with the ability of the BDIAM model to integrate global information. Additionally, by simultaneously performing IDH genotyping and glioma segmentation tasks, BMC-Net enables the sharing and optimization of feature representations across tasks, further enhancing performance. The outcomes of the experiments demonstrate that BMC-Net surpasses traditional methods in terms of AUC and accuracy, offering strong support for personalized treatment and prognosis of gliomas.