Advancements in deep generative models have enabled the joint modeling of antibody sequence and structure, given the antigen-antibody complex as context. However, existing approaches for optimizing complementarity-determining regions (CDRs) to improve developability properties operate in the raw data space, leading to excessively costly evaluations due to the inefficient search process. To address this, we propose LatEnt blAck-box Design (LEAD), a sequence-structure co-design framework that optimizes both sequence and structure within their shared latent space. Optimizing shared latent codes can not only break through the limitations of existing methods, but also ensure synchronization of different modality designs. Particularly, we design a black-box guidance strategy to accommodate real-world scenarios where many property evaluators are non-differentiable. Experimental results demonstrate that our LEAD achieves superior optimization performance for both single and multi-property objectives. Notably, LEAD reduces query consumption by a half while surpassing baseline methods in property optimization. The code is available at https://github.com/EvaFlower/LatEnt-blAck-box-Design.