gas component in the target PNs.]{} [For the case of NGC6781, the broadband maps confirm the nearly pole-on barrel structure of the amorphous carbon-richdust shell and the surrounding halo having temperatures of 26–40K. The PACS/SPIRE multi-position spectra show spatial variations of far-IR lines that reflect the physical stratification of the nebula. We demonstrate that spatially-resolved far-IR line diagnostics yield the ($T_{\rm e}$, $n_{\rm e}$) profiles, from which distributions of ionized, atomic, and molecular gases can be determined. Direct comparison of the dust and gas column mass maps constrained by the HerPlaNS data allows to construct an empirical gas-to-dust mass ratio map, which shows a range of ratios with the median of $195\pm110$. The present analysis yields estimates of the total mass of the shell to be 0.86M$_{\odot}$, consisting of 0.54M$_{\odot}$ of ionized gas, 0.12M$_{\odot}$ of atomic gas, 0.2M$_{\odot}$ of molecular gas, and $4\times10^{-3}$M$_{\odot}$ of dust grains. These estimates also suggest that the central star of about 1.5M$_{\odot}$ initial mass is terminating its PN evolution onto the white dwarf cooling track.]{} [The HerPlaNS data provide various diagnostics for both the dust and gas components in a spatially-resolved manner. In the forthcoming papers of the HerPlaNS series we will explore the HerPlaNS 