Imaging signals derived from the atomic force microscope (AFM) are typically presented as separate adjacent images with greyscale or pseudo-colour palettes. We propose that information-rich false-colour composites are a useful means of presenting three-channel AFM image data. This method can aid the interpretation of complex surfaces and facilitate the perception of information that is convoluted across data channels. We illustrate this approach with images of filamentous cyanobacteria imaged in air and under aqueous buffer, using both deflection-modulation (contact) mode and amplitude-modulation (tapping) mode. Topography-dependent contrast in the error and tertiary signals aids the interpretation of the topography signal by contributing additional data, resulting in a more detailed image, and by showing variations in the probe-surface interaction. Moreover, topography-independent contrast and topography-dependent contrast in the tertiary data image (phase or friction) can be distinguished more easily as a consequence of the three dimensional colour-space.