Plant cells are surrounded by rigid walls, which are multilayered and heterogeneous structures consisting of a soft polymer matrix reinforced with stiff cellulose microfibrils. Research has highlighted the role of mechanical forces acting on the cell wall in the regulation of plant cell growth. Microfibril reorientation during cell expansion has emerged as a key factor influencing morphogenesis through its effect on apparent wall properties. In this work, we develop a model that couples cell growth to the mechanics and synthesis of a heterogeneous and multilayered wall. To do this, we use various concepts from the literature on fibre-reinforced polymers. In particular, we use the Halpin-Tsai equations to predict elastic properties and the Tsai-Hill criterion to predict plastic yield. Our model provides insight into cell growth dynamics, wall stress profiles, apparent wall properties and the effect of key parameters such as microfibril volume fraction and aspect ratio on these results.