I don't know if we regard the following as having more 'kedusha' per se, but from a practical halacha perspective there is an instance where we value a printed tanach above that of a printed Chumash.
Building on my comment, as far as leining a haftarah, the Magen Avraham 284:1 and the Taz 284:2 write that it is preferable to use a sefer tanach over a chumash that has the haftarah of that week's portion at the back.
The Mishnah Berurah 284:1 gives a good summary here. The main thrust is that the Taz and Magen Avraham permit reading the Haftorah from something printed and the Magen Avraham and Eliyahu Rabah require a full Navi. Haftoros in a printed Chumash should be ideally avoided. However, (thank you @DoubleAA for clarification), if there is no full Navi, one can be meikel (lenient), and not miss out the Haftarah.