Recent observations indicate that many, if not all, galaxies host massive central black holes (BHs). In this paper, we explore the influence of supermassive binary black holes (SMBBHs) on their actions as gravitational lenses. When lenses are modelled as singular isothermal ellipsoids, binary BHs change the critical curves and caustics differently as a function of distance. Each BH can in principle create at least one additional image, which, if observed, provides evidence of BHs. By studying how SMBBHs affect the cumulative distribution of magnification for images created by BHs, we find that the cross-section for at least one such additional image to have a magnification larger than 10−5 is comparable to the cross-section for producing multiple images in singular isothermal lenses. Such additional images may be detectable with high-resolution and large dynamic range maps of multiply imaged systems from future facilities, such as the Square Kilometre Array. The probability of detecting at least one image (two images) with magnification above 10−3 is ∼0.2fBH (∼0.05fBH) in a multiply imaged lens system, where fBH is the fraction of galaxies housing binary BHs. We also study the effects of SMBBHs on the core images when galaxies have shallower central density profiles (modelled as non-singular isothermal ellipsoids). We find that the cross-section of the usually faint core images is further suppressed by SMBBHs. Thus, their presence should also be taken into account when one constrains the core radius from the lack of central images in gravitational lenses.