Novae are some of the most commonly detected optical transients and have the potential to provide valuable information about binary evolution. Binary population synthesis codes have emerged as the most effective tool for modelling populations of binary systems, but such codes have traditionally employed greatly simplified nova physics, precluding detailed study. In this work, we implement a model treating H and He novae as individual events into the binary population synthesis code binaryc. This treatment of novae represents a significant improvement on the `averaging treatment currently employed in modern population synthesis codes. We discuss the evolutionary pathways leading to these phenomena and present nova event rates and distributions of several important physical parameters. Most novae are produced on massive white dwarfs, with approximately 70 and 55 per cent of nova events occurring on O/Ne white dwarfs for H and He novae respectively. Only 15 per cent of H-nova systems undergo a common-envelope phase, but these systems are responsible for the majority of H nova events. All He-accreting He-nova systems are considered post-common-envelope systems, and almost all will merge with their donor star in a gravitational-wave driven inspiral. We estimate the current annual rate of novae in M31 (Andromeda) to be approximately $41 pm 4$ for H novae, underpredicting the current observational estimate of $65^{+15}_{-16}$, and $0.14pm0.015$ for He novae. When varying common-envelope parameters, the H nova rate varies between 20 and 80 events per year.
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