In this paper, we analyze the interconnectedness between investor sentiment and stock price jumps based on the two-layer network models. We first use the Diebold and Yilmaz (DY) and Baruník and Křehlík (BK) spillover indexes to analyze the interactive effects of investor sentiment and price jumps between different industries in China's carbon–neutral sectors from the time and frequency domains. The results verify strong two-way spillover effects of investor sentiment and jump volatility among green industries. The connectedness in the short-term risk network of stock volatility is significantly higher than that of the Internet sentiment network, and the short-term risk spillover effect of the network plays a leading role in the total risk spillover. Subsequently, we further study the dynamic spillover between investor sentiment and jump volatility using the rolling time window. The dynamic network reveals significant heterogeneity in the spillover of Internet sentiment, and the interaction effect of investor sentiment and jump volatility displays time-varying characteristics. The green industrials and energy industries are systemically important sectors in the two-layer network system. The empirical results show the complex risk contagion mode in the green stock market and provide a reference for investors and market regulators on the risk management of the green stock market.