Circumstellar dust discs have been observed around many nearby stars. However, many stars are part of binary or multiple stellar systems. A natural question arises regarding the presence and properties of such discs in systems with more than one star. To address this, we consider a sample of 449 systems (spectral types A-M) observed with the Herschel Space Observatory as part of the DEBRIS (Disc Emission via a Bias-free Reconnaissance in the Infrared/Submillimetre) programme. We have examined the stellar multiplicity of this sample by gathering information from the literature and performing an adaptive optics imaging survey at Lick Observatory. Five new companions were revealed with our programme. In total, we identify 188 (42 per cent) binary or multiple star systems. The multiplicity of the sample is examined with regards to the detection of circumstellar discs for stars of spectral types AFGK. In general, discs are less commonly detected around binaries than single stars, though the disc frequency is comparable among A stars regardless of multiplicity. However, this sample reveals the period distribution of disc-bearing binaries is consistent with that of non-disc binaries and with comparison field samples. We find that the properties of discs in binary systems are not statistically different from those around single stars. Although the frequency of disc-bearing FGK binaries may be lower than in single star systems, the processes behind disc formation and the characteristics of these discs are comparable among both populations.