This study assesses the non-linear effects of green bonds, conventional bonds and energy commodities on the behaviour of the cap-and-trade European Union carbon market (European Union Emissions Trading System [EU-ETS]). By estimating four models, using Markov-switching (MS) econometric methodology, non-linearities are confirmed in dynamic behaviours, observing in the global calculation a positive effect of green bonds (S&P Green and Sol Green) on the carbon market, in regimes of both high and low volatility, whereas conventional bonds (S&P Agg) and energy commodities (DJCI En) contribute to a decrease in the carbon market in regimes of high volatility. The relevance of green bonds is underlined in determining the behaviour of the carbon market, besides observing greater persistence of the low volatility regime. These results allow both investors and fund managers to implement strategies in different volatility or economic activity contexts through a diversified portfolio and green/climate structure.