Jovian Trojan D-type asteroids have mid-infrared emissivity features strikingly similar to comet comae, suggesting that they have the same compositions and that the surfaces of the Trojans are highly porous. However, a direct comparison between a comet and asteroid surface has not been possible due to the paucity of spectra of comet nuclei at mid-infrared wavelengths. We present 5-35 {mu}m thermal emission spectra of comets 10P/Tempel 2, and 49P/Arend-Rigaux observed with the Infrared Spectrograph on the Spitzer Space Telescope. Our analysis suggests the spectra are dominated by the comet nucleus. We fit each spectrum with the near-Earth asteroid thermal model (NEATM) and find sizes in agreement with previous values. However, the NEATM beaming parameters of the nuclei, 0.74 to 0.83, are systematically lower than the Jupiter-family comet population mean of 1.03+/-0.11, derived from 16- and 22-{mu}m photometry. When the spectra are normalized by the NEATM model, a weak 10-{mu}m silicate plateau is evident, with a shape similar to those seen in mid-infrared spectra of D-type asteroids. We compare, in detail, these comet nucleus emission features to those seen in spectra of the Jovian Trojan D-types (624) Hektor, (911) Agamemnon, and (1172) Aneas, as well as those seen in the spectra of seven comet comae. The comet comae present silicate features with two distinct shapes, either trapezoidal, or more rounded. The surfaces of Tempel 2, Arend-Rigaux, and Hektor best agree with the comae that present trapezoidal features. An emissivity minimum at 15 {mu}m, present in the spectra of Tempel 2, Arend-Rigaux, Hektor, and Agamemnon, is also described, the origin of which remains unidentified. The compositional similarity between D-type asteroids and comets is discussed, and our data supports the hypothesis that they have similar origins in the early Solar System.