This study proposes an original Physics-Informed Dual Neural Networks (PIDNN) framework to efficiently predict the complex mechanical behaviors of rubber composites under equibiaxial and planar tension, addressing a key challenge in rubber product simulation. The framework strategically integrates accessible uniaxial tensile data with physics-informed constraint from a calibrated Yeoh hyperelastic model. Through two coupled neural networks (ANN-A and ANN-B), the framework iteratively resolves complete stress-strain responses: ANN-A predicts equibiaxial stress using uniaxial test data and Yeoh-derived planar stress, while ANN-B subsequently determines planar tension stress using uniaxial and the newly predicted equibiaxial data. The PIDNN model demonstrates excellent predictive performance when validated against independent experimental datasets. Furthermore, its robustness and generalizability are successfully verified through applications to several representative rubber composites.