Generative protein modeling offers tools for designing diverse protein sequences and structures, but achieving high protein stability remains challenging. Jointly optimizing P(structure|sequence) and P(sequence|structure), allows models to explore the full energy landscape and find the optimal solution. In this study, we tackled two key aspects of stable protein design: stable protein generation and stability scoring.For both tasks, we employed a joint structure-sequence modeling approach, which outperformed models based solely on sequence or structure. Experimental validations show that our joint TrROS (TrRosetta) and TrMRF model generated the most stable proteins with the lowest Δ G_fold, while our hybrid scoring matrix (ESMFold pLDDT + ESM2 Pseudo-likelihood) predicted stability with the highest accuracy. These findings highlight the potential of our end-to-end approach of joint optimization for generating and ranking stable proteins.