In times of crisis, such as global pandemics or conflicts, investors’ preference between green and conventional bonds may lean towards the latter due to increased risk aversion and a focus on short-term stability. However, some investors motivated by increased awareness of sustainability issues may maintain or increase their allocation to green bonds, seeing them as an opportunity for long-term resilience and sustainable investing. We use multifractal detrended cross-correlation analysis, wavelet coherence, and copula-based dependence analysis to examine the complex relationship between the S&PGreen Bond Index and the S&P500 Bond Index. The results indicate the presence of multifractal cross-correlations, the strength of which is most pronounced in times of crisis, especially in the post-COVID-19 period. The wavelet-based analysis also detects the COVID-19 break and shows significant interdependence at all frequency levels after the RU–UA conflict. The copula-based correlation values exhibit a distinct oscillating pattern over time, characterized by an initial break coinciding with the impact of COVID-19. In light of these findings on the impact of COVID-19 and the RU–UA conflict, we have included the Geopolitical Risk Index in our analysis to better understand how geopolitical tensions and conflicts influence the observed interdependence and to gain insight into how changes in the global risk environment affect both bond market dynamics. Overall, the results of this study provide insights into the interconnectedness between conventional and green bond markets and highlight potential spillover effects and systemic risks in an increasingly complex financial landscape.