We compile a sample of 341 binary and multiple star systems with the aim of searching for and characterizing Kuiper belt-like debris discs. The sample is assembled by combining several smaller samples studied in previously published work with targets from two unpublished Herschel surveys. We find that 38 systems show excess emission at 70 or 100{mu}m suggestive of a debris disc. While nine of the discs appear to be unstable to perturbations from their host binary based on a simple analysis of their inferred radii, we argue that the evidence for genuine instability is not strong, primarily because of uncertainty in the true disc radii, uncertainty in the boundaries of the unstable regions, and orbital projection effects. The binary separation distributions of the disc-bearing and disc-free systems are different at a confidence level of 99.4 per cent, indicating that binary separation strongly influences the presence of detectable levels of debris. No discs are detected for separations between ~25 and 135au; this is likely a result of binaries whose separations are comparable with typical disc radii clearing out their primordial circumstellar or circumbinary material via dynamical perturbations. The disc detection rate is 19^+5^_-3_ per cent for binaries wider than 135au, similar to the published results for single stars. Only 8^+2^_-1_ per cent of systems with separations below 25au host a detectable disc, which may suggest that planetesimal formation is inhibited in binaries closer than a few tens of au, similar to the conclusions of studies of known planet-hosting binaries.