The transition toward cognitive global navigation satellite system (GNSS) receivers requires accurate interference classification to trigger adaptive mitigation strategies. However, conventional methods relying on Time-Frequency Analysis (TFA) and Convolutional Neural Networks (CNNs) face two fundamental limitations: severe performance degradation in low Jamming-to-Signal Ratio (JSR) regimes due to noise obscuration, and ``feature degeneracy'' caused by the loss of phase information in magnitude-only spectrograms. Consequently, spectrally similar signals -- such as high-order Quadrature Amplitude Modulation versus Band-Limited Gaussian Noise -- become indistinguishable. To overcome these challenges, this paper proposes the \textbf{JSR-Guided Fusion Network (JSR-GFNet)}. This multi-modal architecture combines phase-sensitive complex In-Phase/Quadrature (IQ) samples with Short-Time Fourier Transform (STFT) spectrograms. Central to this framework is a physics-inspired dynamic gating mechanism driven by statistical signal descriptors. Acting as a conditional controller, it autonomously estimates signal reliability to dynamically reweight the contributions of a Complex-Valued ResNet (IQ stream) and an EfficientNet backbone (STFT stream). To validate the model, we introduce the Comprehensive GNSS Interference (CGI-21) dataset, simulating 21 jamming categories including software-defined waveforms from aerial platforms. Extensive experiments demonstrate that JSR-GFNet achieves higher accuracy across the full 10--50 dB JSR spectrum. Notably, interpretability analysis confirms that the model learns a physically intuitive strategy: prioritizing spectral energy integration in noise-limited regimes while shifting focus to phase precision in high-SNR scenarios to resolve modulation ambiguities. This framework provides a robust solution for next-generation aerospace navigation security.