High-resolution range profile (HRRP)-based radar automatic target recognition suffers from severe performance degradation in composite jamming environments. Active jamming introduces suppression- and deception-related components into the received range profile. After pulse compression, these components are coupled with target echoes in the HRRP domain, making target-related scattering peaks difficult to distinguish and weakening feature separability. To address this problem, this paper proposes JointHRRP-Net, a unified framework for joint target-jamming recognition. A statistically constrained decoupling module is first developed to generate target-dominant and jamming-dominant latent branches from the mixed HRRP representation. Correlation-guided statistical constraints are imposed to suppress redundant cross-branch information and alleviate target-jamming feature entanglement. A multi-scale temporal encoding module is then designed to model local scattering structures and long-range range-cell dependencies, followed by a dual-expert decision module for single-label target classification and multi-label jamming classification. Experiments under diverse signal-to-jamming ratio (SJR) and signal-to-noise ratio (SNR) levels demonstrate that JointHRRP-Net outperforms representative baseline methods in both target recognition and composite jamming recognition. Open-set evaluation further shows that the learned target representation remains discriminative for unknown-target rejection. These results demonstrate the effectiveness and robustness of JointHRRP-Net in composite jamming scenarios.