This paper introduces a novel multi-moment connectedness network approach for analyzing the interconnectedness of green financial market. Focusing on the impact of monetary policy shocks, our study reveals that connectedness within the green bond and equity markets varies with different moments (returns, volatility, skewness, and kurtosis) and changes significantly around Federal Open Market Committee (FOMC) events. Static analysis shows a decrease in connectedness with higher moments, while dynamic analysis highlights increased sensitivity to event-driven shocks. We find that both tight and loose monetary policy shocks initially elevate connectedness within the first six months. However, the effects of tight shocks gradually fade, whereas loose shocks may reduce connectedness after one year. These results offer insight to policymakers in regulating sustainable economies and investment managers in strategizing asset allocation and risk management, especially in environmentally focused markets. Our study contributes to understanding the complex dynamics of the green financial market in response to monetary policies, helping in decision-making for sustainable economic development and financial stability.