Sound event detection (SED) and acoustic scene classification (ASC) are critical tasks in computational environmental sound scene analysis. Both exhibit significant potential across diverse applications, including urban environment detection, smart home integration, and anomaly monitoring. Considering the intricate relationship between acoustic scenes and sound events, researchers have proposed a joint analysis method for SED and ASC tasks using multi-task learning (MTL). However, conventional MTL-based methods rely mainly on a hard parameter-sharing mechanism, which restricts information flow and collaborative learning among tasks during training. To address this issue, this paper proposes a novel MTL method for SED that employs a soft parameter-sharing mechanism to explore the intrinsic correlation between acoustic scenes and sound events. A cross-stitch mechanism is introduced in this study to facilitate soft parameter-sharing between the SED and ASC tasks by employing scene information to improve the performance of the SED tasks and ensure training efficiency. Furthermore, a dual-stream attention convolution module (DACM) is designed to capture global and local contextual information through parallel branches of attention and convolution. To evaluate the performance of the proposed method in SED tasks, we tested two datasets: the TUT Acoustic Scenes 2016/2017 and TUT Sound Events 2016/2017 datasets and the synthetic sound scene datasets. Experimental results indicate that the proposed MTL method outperforms state-of-the-art approaches, demonstrating that acoustic scene information can improve the performance of SED tasks.