We present sub-arcsecond 7.5$-$13 $mu$m imaging- and spectro-polarimetric observations of NGC 1068 using CanariCam on the 10.4-m Gran Telescopio CANARIAS. At all wavelengths, we find: (1) A 90 $times$ 60 pc extended polarized feature in the northern ionization cone, with a uniform $sim$44$^{circ}$ polarization angle. Its polarization arises from dust and gas emission in the ionization cone, heated by the active nucleus and jet, and further extinguished by aligned dust grains in the host galaxy. The polarization spectrum of the jet-molecular cloud interaction at $sim$24 pc from the core is highly polarized, and does not show a silicate feature, suggesting that the dust grains are different from those in the interstellar medium. (2) A southern polarized feature at $sim$9.6 pc from the core. Its polarization arises from a dust emission component extinguished by a large concentration of dust in the galaxy disc. We cannot distinguish between dust emission from magnetically aligned dust grains directly heated by the jet close to the core, and aligned dust grains in the dusty obscuring material surrounding the central engine. Silicate-like grains reproduce the polarized dust emission in this feature, suggesting different dust compositions in both ionization cones. (3) An upper limit of polarization degree of 0.3 per cent in the core. Based on our polarization model, the expected polarization of the obscuring dusty material is $lesssim$0.1 per cent in the 8$-$13 $mu$m wavelength range. This low polarization may be arising from the passage of radiation through aligned dust grains in the shielded edges of the clumps.
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