We present absorption line strength maps for a sample of 18 Sb-Sd galaxies observed using the integral-field spectrograph SAURON operating at the William Herschel Telescope on La Palma, as part of a project devoted to the investigation of the kinematics and stellar populations of late-type spirals, a relatively unexplored field. The SAURON spectral range allows the measurement of the Lick/IDS indices Hβ, Fe5015 and Mgb, which can be used to estimate the stellar population parameters. We present here the two-dimensional line strength maps for each galaxy. From the maps, we learn that late-type spiral galaxies tend to have high Hβ and low Fe5015 and Mgb values, and that the Hβ index has often a positive gradient over the field, while the metal indices peak in the central region. We investigate the relations between the central line strength indices and their correlations with morphological type and central velocity dispersion, and compare the observed behaviour with that for ellipticals, lenticulars and early-type spirals from the SAURON survey. We find that our galaxies lie below the Mg-σ relation determined for elliptical galaxies and that the indices show a clear trend with morphological type. From the line strength maps we calculate age, metallicity and abundance ratio maps via a comparison with model predictions; we discuss the results from a one-SSP (single stellar population) approach and from a two-SSP approach, considering the galaxy as a superposition of an old (~13 Gyr) and a younger (age <=5 Gyr) population. We confirm that late-type galaxies are generally younger and more metal-poor than ellipticals and have abundance ratios closer to solar values. We also explore a continuous star formation scenario, and try to recover the star formation history using the evolutionary models of Bruzual & Charlot, assuming constant or exponentially declining star formation rate. In this last case, fixing the galaxy age to 10 Gyr, we find a correlation between the e-folding time-scale τ of the starburst and the central velocity dispersion, in the sense that more massive galaxies tend to have shorter τ, suggesting that the star formation happened long ago and has now basically ended, while for smaller objects with larger values of τ it is still active now.