The Neural Engineering Framework (NEF) is a theory for mapping computations onto biologically plausible networks of spiking neurons. This theory has been applied to a number of neuromorphic chips. However, within both silicon and real biological systems, synapses exhibit higher-order dynamics and heterogeneity. To date, the NEF has not explicitly addressed how to account for either feature. Here, we analytically extend the NEF to directly harness the dynamics provided by heterogeneous mixed-analog-digital synapses. This theory is successfully validated by simulating two fundamental dynamical systems in Nengo using circuit models validated in SPICE. Thus, our work reveals the potential to engineer robust neuromorphic systems with well-defined high-level behaviour that harness the low-level heterogeneous properties of their physical primitives with millisecond resolution.