Sign languages are multi-channel languages that communicate information through not just the hands (manual signals) but also facial expressions and upper body movements (non-manual signals). However, since automatic sign language translation is usually performed by generating a single sequence of glosses, researchers eschew non-manual and co-occurring manual signals in favor of a simplified list of manual glosses. This can lead to significant information loss and ambiguity. In this paper, we introduce a new task named multi-channel sign language translation (MCSLT) and present a novel metric, SignBLEU, designed to capture multiple signal channels. We validated SignBLEU on a system-level task using three sign language corpora with varied linguistic structures and transcription methodologies and examined its correlation with human judgment through two segment-level tasks. We found that SignBLEU consistently correlates better with human judgment than competing metrics. To facilitate further MCSLT research, we report benchmark scores for the three sign language corpora and release the source code for SignBLEU at https://github.com/eq4all-projects/SignBLEU.