Application logic is inherently distributed between client and server due to the fundamental Client/Server architecture of the Web. The individual distribution is specified at design time and remains unchanged stable, preventing individual load distribution between clients and server at runtime. Dynamic code mobility at runtime, in contrast, allows to balance the needs of users, through increased responsiveness, and software providers, through better resource usage and cost reductions. Enabled by WebAssembly, the Web ecosystem recently provides the technological foundation for relocating code units during runtime. However, leveraging these capabilities to enhance web applications with dynamic code migration presents challenges for web engineers. In response, we propose an innovative distributed Client/Server software architecture for web applications. This architecture facilitates the dynamic migration of code at runtime, and addresses the technical challenges like dependency management, control and data flow distribution, communication, and interfaces. This novel software architecture serves as a reference for web engineers aiming to enrich their web applications with dynamic code mobility. Additionally, it contributes to the ongoing reevaluation of the Web ecosystem in light of the widespread adoption and standardization of WebAssembly across major browsers. Through experimentation in four scenarios, we demonstrate the feasibility of implementing this architecture, its negligible impact on performance and the optimization potential for individual code distributions across client and server.