In this work, we introduce a two-tier control architecture for nonlinear process systems with both continuous and asynchronous sensing and actuation. This class of systems arises naturally in the context of process control systems based on hybrid communication networks (i.e. point-to-point wired links integrated with networked wired or wireless communication) and utilising multiple heterogeneous measurements (e.g. temperature and concentration). Assuming that there exists a lower-tier control system which relies on point-to-point communication and continuous measurements to stabilise the closed-loop system, we propose to use Lyapunov-based model predictive control to design an upper-tier networked control system to profit from both the continuous and the asynchronous measurements as well as from additional networked control actuators. The proposed two-tier control system architecture preserves the stability properties of the lower-tier controller while improving the closed-loop performance. The theoretical results are demonstrated using two different chemical process examples.