Aims. We investigate the dust-to-gas mass ratio and the environmental effects on the various components of the interstellar medium for a spatially resolved sample of Virgo spirals. Methods. We have used the IRAM-30 m telescope to map over their full extent NGC 4189, NGC 4298, NGC 4388, and NGC 4299 in the 12CO(1-0) and the 12CO(2-1) lines. We observed the same lines in selected regions of NGC 4351, NGC 4294, and NGC 4424. The CO observations are combined with Herschel maps in 5 bands between 100-500 μm from the HeViCS survey, and with HI data from the VIVA survey, to obtain spatially resolved dust and gas distributions. We studied the environmental dependencies by adding to our sample eight galaxies with 12CO(1-0) maps from the literature. Results. We estimate the integrated mass of molecular hydrogen for the galaxies observed in the CO lines.We find molecular-to-total gas mass fractions between 0.04 ≤ f mol ≤ 0.65, with the lowest values for the dimmest galaxy in the B-band. The integrated dust-togas ratio ranges between 0.011 and 0.004. For the 12 mapped galaxies we derive the radial distributions of the atomic gas, molecular gas, and dust. We also study the effect of different CO-to-H2 conversion factors. Both the molecular gas and the dust distributions show steeper radial profiles for HI-deficient galaxies and the average dust-to-gas ratio for these galaxies increases or stays radially constant. On scales of ∼3 kpc, we find a strong correlation between the molecular gas and the 250 μm surface brightness that is tighter than average for non-deficient galaxies. The correlation becomes linear if we consider the total gas surface mass density. However, the inclusion of atomic hydrogen does not improve the statistical significance of the correlation. Conclusions. The environment can modify the distributions of molecules and dust within a galaxy, although these components are more tightly bound than the atomic gas. © ESO, 2012.