As the electromagnetic environment becomes increasingly complex, Global Navigation Satellite Systems (GNSS) face growing threats from sophisticated jamming interference. Although Deep Learning (DL) effectively identifies basic interference, classifying compound interference remains difficult due to the superposition of diverse jamming sources. Existing single-domain approaches often suffer from performance degradation because transient burst signals and continuous global signals require conflicting feature extraction scales. We propose the Selective Kernel and Asymmetric convolution Network(SKANet), a cognitive deep learning framework built upon a dual-stream architecture that integrates Time-Frequency Images (TFIs) and Power Spectral Density (PSD). Distinct from conventional fusion methods that rely on static receptive fields, the proposed architecture incorporates a Multi-Branch Selective Kernel (SK) module combined with Asymmetric Convolution Blocks (ACBs). This mechanism enables the network to dynamically adjust its receptive fields, acting as an adaptive filter that simultaneously captures micro-scale transient features and macro-scale spectral trends within entangled compound signals. To complement this spatial-temporal adaptation, a Squeeze-and-Excitation (SE) mechanism is integrated at the fusion stage to adaptively recalibrate the contribution of heterogeneous features from each modality. Evaluations on a dataset of 405,000 samples demonstrate that SKANet achieves an overall accuracy of 96.99\%, exhibiting superior robustness for compound jamming classification, particularly under low Jamming-to-Noise Ratio (JNR) regimes.