We analyse V- and H-band surface photometry of a sample of 18 Sb-Sd galaxies. Combining high-resolution Hubble Space Telescope (HST) images with ground-based near-infrared observations, we extract photometric profiles, which cover the whole disc and provide the highest possible resolution. This is the first photometric study of late-type spirals for which the stellar kinematics have been measured. For 10 out of the 18 galaxies, HST data in both F160W (H) and F606W (V) are available, and, for those, we present colour maps and radial colour profiles at the resolution of the HST. Colours vary significantly from galaxy to galaxy, but tend to be highly homogeneous within each galaxy, with smooth and flat colour profiles. Some of the colour maps show jumps in the inner regions, likely due to dust. We determine extinction maps in an almost model-independent way using the V - H colour map and the SAURON Mgb absorption line map of Ganda et al. The maps show that AV ranges from 0 to 2 mag, in the centre from 0 to 1.5 mag, in agreement with the models of Tuffs et al. We describe the surface brightness profiles as the superposition of an exponential disc and a Sérsic bulge. The bulges are small (0.1-2.5 kpc), and show a shape parameter n ranging from ~0.7 to 3, with a mean value smaller than two: well below the value for the classical de Vaucouleurs bulges. Most galaxies (16 out of 18) show a central light excess above the Sérsic fit to the bulge, which can be interpreted as a nuclear cluster, as shown by previous studies. We provide zero-order estimates for the magnitude of these components. We discuss the correlations among the structural galaxy parameters and with other relevant quantities, such as Hubble type and stellar velocity dispersion. We compare these results with a recent paper by Graham & Worley, who present a summary of most of the NIR surface photometry of spirals in the literature. For both early- and late-type spirals, bulge luminosity strongly correlates with central velocity dispersion; at constant velocity dispersion, later type bulges are larger and less dense, and have lower Sérsic n-values.