The purpose of this work is the characterization of the main scaling relations between all the ISM components (dust, atomic/molecular/total gas), gas-phase metallicity, and other galaxy properties, such as Mstar and galaxy morphology, for late-type galaxies in the Local Universe. This study is performed by extracting late-type galaxies from the entire DustPedia sample and by exploiting the large and homogeneous dataset available thanks to the DustPedia project. The sample consists of 436 galaxies with morphological stage from T = 1 to 10, Mstar from 6 x 10^7 to 3 x 10^11 Msun, SFR from 6 x 10^(-4) to 60 Msun/yr, and 12 + log(O/H) from 8 to 9.5. The scaling relations involving the molecular gas are studied by assuming both a constant and a metallicity-dependent XCO. The analysis has been performed by means of the survival analysis technique. We confirm that the dust mass correlates very well with the total gas mass, and find -- for the first time -- that the dust mass correlates better with the atomic gas mass than the molecular one. We characterize important mass ratios such as gas fraction, molecular-to-atomic gas mass ratio, dust-to-total gas mass ratio (DGR), and dust-to-stellar mass ratio. Only the assumption of a metallicity-dependent XCO reproduces the expected decrease of the DGR with increasing morphological stage and decreasing gas-phase metallicity, with a slope of about 1. DGR, gas-phase metallicity, and the dust-to-stellar mass ratio are, for our galaxy sample, directly linked to the galaxy morphology. The molecular-to-atomic gas mass ratio and the DGR show a positive correlation for low molecular gas fractions, but for molecular gas rich galaxies this trend breaks down. This trend has never been found previously, to our knowledge. It provides new constraints for theoretical models of galaxy evolution and a reference for high-redshift studies.