Well if i get this right, rel=author links to your private and personal Google+ page. And the rel=publisher tag links to your Google+ business page. I think it's not possible to use both of them, because you're trying to mix a google+ profile and business page.
Edit (short): It's possible
Edit (long): It's possible, because with the rel=publisher you confirm that the website is the publisher (of the given g+ page) and the rel=author confirms that you're the author (of the content). These snippets are very useful if you're having a website with multi-authorship.