We investigate the connection between dust and gas in the nearby edge-on spiral galaxy NGC 891, a target of the Very Nearby Galaxies Survey. High resolution Herschel PACS and SPIRE 70, 100, 160, 250, 350, and 500 mu m images are combined with JCMT SCUBA 850 mu pm observations to trace the far-infrared/submillimetre spectral energy distribution (SED). Maps of the HI 21 cm line and CO(J = 3-2) emission trace the atomic and molecular hydrogen gas, respectively. We tit one-component modified blackbody models to the integrated SED, finding a global dust mass of (8.5 2.0) x 10(7) M-circle dot, and an average temperature of 23 +/- 2 K. consistent with results from previous far-infrared experiments. We also fit one-component modified blackbody models to pixel-by-pixel SEDs to produce maps of the dust mass and temperature. The dust mass distribution correlates with the total stellar population as traced by the 3.6 pm emission. The derived dust temperature, which ranges from approximately 17 to 24 K, is found to correlate with the 24 mu m emission. Allowing the dust emissivity index to vary, we find an average value of beta = 1.9 +/- 0.3. We confirm an inverse relation between the dust emissivity spectral index and dust temperature, but do not observe any variation of this relationship with vertical height from the mid-plane of the disc. A comparison of the dust properties with the gaseous components of the ISM reveals strong spatial correlations between the surface mass densities of dust (Sigma(dust)) and the molecular hydrogen (Sigma H-2) and total gas surface densities (Sigma(gas)," These observations reveal the presence of regions of dense, cold dust that are coincident with peaks in the gas distribution and are associated with a molecular ring. Furthermore, the observed asynunetries in the dust temperature, the H2-to-dust ratio and the total gas-to-dust ratio hint that an enhancement in the star formation rate may be the result of larger quantities of molecular gas as to fuel star formation in the NE compared to the SW. Whilst the asymmetry likely arises from dust obscuration due to the geometry of the line-of-sight projection of the spiral arms, we cannot exclude that there is also an enhancement in the star formation rate in the NE part of the disc.