We propose CLASS; a novel unified model for the synthesis and search for design layouts, two tasks that are often handled separately by prior works. We propose to learn a compact and coherent latent feature of a layout supporting joint search and synthesis. This allows various operations such style-conditioned layout generation, latent space manipulation and provides seamless integration of search and synthesis for an effective design workflow. We train CLASS with a dual decoder: a new transformerbased layout-conditioned decoder and a CNN-based raster decoder. The latent-conditioned decoder explicitly conditions upon a latent vector while generating a layout in an auto-regressive fashion. We train CLASS under variational framework which in conjunction with a raster-decoder enhances the latent representation improving both generation and retrieval performances. We show the effectiveness of CLASS on the RICO and PubLayNet benchmarks, and demonstrate that CLASS is capable of high-quality synthesis from scratch, as well as performing self-completion, interpolation, project between design layouts, whilst achieving close to or better than state-of-the-art search performance.