The Heath-Jarrow-Morton model is an important tool for describing the term structure of interest rates. A regime switching version was considered by Elliott and Siu (Quant Finance 16(12):1791–1800, 2016). It is of interest to price the risk due to the regime switching and this was discussed in Elliott and Siu (Quant Finance 16(12):1791–1800, 2016). In this paper, an extended Heath-Jarrow-Morton model for stochastic forward rates, incorporating both regime shifts and jumps is considered, where jumps in the forward rate dynamics are directly triggered by the regime switches. No-arbitrage drift conditions, which take into account the pricing of both the regime-switching and jump risks, are derived in two situations. The first situation starts with a risk-neutral measure while the second situation starts with the real-world measure.