We have obtained deep optical spectra of the planetary nebula NGC 6153, both along its minor axis and by uniformly scanning a long slit across the whole nebula. The scanned spectra, when combined with the nebular total Hβ flux, yield integrated fluxes for all the lines (~400) in our spectra, which are rich in strong recombination lines from C, N, O and Ne ions. A weak OVI λ3811 emission line from the central star has been detected, suggesting that the nucleus of NGC 6153 has a hydrogen-deficient surface. The optical data, together with the ISO LWS 43-197μm spectrum and the archival IUE and IRAS LRS spectra, are used to study the thermal and density structure and to derive the heavy-element abundances from lines produced by different excitation mechanisms. In all cases, the C2+/H+, N2+/H+, O2+/H+ and Ne2+/H+ abundances derived from multiple optical recombination lines (ORLs) are consistently higher, by about a factor of 10, than the corresponding values deduced from optical, UV or infrared (IR) collisionally excited lines (CELs), regardless of the excitation energies or critical densities of the latter. The agreement between the temperature-sensitive optical forbidden lines and the temperature-insensitive IR fine-structure lines rules out temperature fluctuations as the cause of the large difference between the ORL and CEL abundances. We present the results of a new calculation of recombination coefficients for [OII] which lead to good agreement between the observed and predicted [OII] λλ7320,7330 forbidden line intensities if these lines are solely excited by recombination at the Balmer jump temperature. Recombination excitation is also found to be important in exciting the [NII] λ5754 line, which, if unaccounted for, would lead to an overestimated [NII] temperature from the observed (λ6548+λ6584)/λ5754 ratio. Analysis of a number of CII lines arising from levels as high as 7g in the recombination ladder reveals excellent agreement between their reddening-corrected relative intensities and those predicted by recombination theory. Spatial analysis of the long-slit spectra taken along the nebular minor axis yields a varying [OIII] temperature, whereas the hydrogen Balmer jump temperature of 6000K is approximately constant across the nebula, and is 2000-3000K lower than the [OIII] temperature. The observed high-n Balmer line decrement indicates that the hydrogen lines arise from material having an electron density of 200020001000 cm-3, consistent with the optical and IR forbidden-line density diagnostics, which yield average line-of-sight electron densities along the minor axis varying between 2000 and 4000cm-3. While the He/H ratio mapped by HeI and HeII recombination lines is constant within 5per cent across the nebula, the C2+/H+ and O2+/H+ recombination-line abundances decrease by a factor of 2-3 over a radius of 15arcsec from the centre, pointing to the presence of abundance gradients. We consider a variety of hypotheses to account for the observed behaviour of the various thermal, density and abundance diagnostics. Empirical nebular models containing two components with differing densities and temperatures are able to account for many of the observed patterns, but only if one of the components is significantly hydrogen-deficient. One such model, which gives a good fit to the observed line intensities and patterns, has 500-K H-depleted material, presumed to be evaporating from dense neutral inclusions, embedded in 9500-K material with `normal' abundances. An alternative model, which appears more physically plausible on a number of grounds, has high-density (2x106cm-3), fully ionized, H-deficient knots embedded in the `normal' component, although this model fails to account adequately for the observed low (6000K) hydrogen Balmer jump temperature. However, the observed fact that the ORLs and CELs yield heavy-element abundance ratios that are identical within the uncertainties finds no obvious explanation in the context of H-deficient knot models.