The transition to a low-carbon economy has elevated green bonds as essential for mobilizing private capital towards sustainable investments. We examine the connectedness between green and conventional bonds across three latent factors of the yield curve. Our results show that green bonds issued by supranational and other public institutions tend to appear as net transmitters during periods of geopolitical or energy-related uncertainty. While green finance remains central to funding, our results indicate that green bonds participate more intensely than conventional bonds in the transmission of stress within fixed-income markets.