Precise interference detection and identification are crucial for enhancing the survivability of communication systems in non-cooperative wireless environments. While deep learning (DL) has advanced this field, existing single-task learning (STL) approaches neglect inherent task correlations. Furthermore, emerging multi-task learning (MTL) methods often lack a theoretical foundation for quantifying and modeling task relationships. To bridge this gap, we establish a theoretically grounded MTL framework for joint interference detection, modulation identification, and interference identification. First, we derive an upper bound for the weighted expected loss in MTL frameworks. This bound explicitly connects MTL performance to task similarity, quantified by the Wasserstein distance and learnable task relation coefficients. Guided by this theory, we present the adversarial multi-task interference detection and identification network (AMTIDIN), which integrates adversarial training to minimize distributional discrepancies across tasks and uses adaptive coefficients to model task correlations dynamically. Crucially, we conducted a quantitative analysis of task similarity to reveal intrinsic task relationships, specifically that modulation identification and interference identification share a substantial feature overlap distinct from interference detection. Extensive comparative experiments demonstrate that AMTIDIN significantly outperforms both its task-specific STL baseline and state-of-the-art MTL baselines in robustness and generalization, particularly under challenging conditions with limited training data, short signal lengths, and low signal-to-noise ratios (SNRs).