Facebook – Are a Facebook profile and Facebook Page Interconnected

You can create a second Facebook account with your business email address and set that account as a co-owner of that Facebook page.

Alternatively, you can setup a auto-forward rule inside Gmail.

Each Facebook Page (brand concept) is administered by one and more flesh-and-blood human beings who have created themselves a personal Facebook Profile: there is no such thing as a personal and a business profile in Facebook, by definition all Profiles are personal.

Now it may be possible to fool Facebook into creating a Profile for a business, but don't waste your time: you are are simply inviting them to delete it once they discover it - for example, when one of your competitors reports it.

Taking a step back, why you are wanting to use the business email for the Facebook - is it because you want to give the password to someone else so that they can also maintain it? If so, then you need to

1. Get their agreement (off-line) to administer the page
2. Get them to use their personal Profile to Like the page Look at the list of people who have Liked your page
3. Choose the person from it, and make them into an administrator.

I know this isn't the answer you want to hear: it's distinctly strange that your business needs to make use of artifacts from people's personal lives to update its communication tools. But I'm afraid that's the way Facebook works, today anyway.