Residential buildings account for about a quarter of the global energy use. As such, residential buildings can play a vital role in achieving net-zero carbon emissions through efficient use of energy and balance of intermittent renewable generation. This chapter presents a co-design framework for simultaneous optimisation of the design and operation of residential buildings using Model Predictive Control (MPC). The adopted optimality criterion maximises cost savings under time-varying electricity prices. By formulating the co-design problem using model predictive control, we then show a way to exploit the use of seasonal storage elements operating on a yearly timescale. A case study illustrates the potential of co-design in enhancing flexibility and self-sufficiency of a system operating on multiple timescales. In particular, numerical results from a low-fidelity model report approximately doubled bill savings and carbon emission reduction compared to the a priori sizing approach.