Dual-colour fluorescence cross-correlation spectroscopy is a powerful method of studying binding between labelled biomolecules in vitro as well as in vivo. However, numerous artefacts and experimental complexities complicate quantitative measurements. Here, we show that a combination of dual-colour fluorescence correlation spectroscopy (FCS) with dual-focus FCS avoids artefacts due to chromatic aberrations or saturation and circumvents the calibration of the detection volumes. In addition, we present a comprehensive mathematical framework that allows us to accurately analyse correlation curves even in the presence of spectral cross-talk, incomplete or stochastic labelling, multiple binding sites, a fluorescent background and depletion due to photobleaching. We demonstrate the merits of this approach using dual-colour dual-focus scanning FCS, which allows binding measurements on membranes not affected by membrane movements.