CI + WordPress

[eluser]CodeIgniterNewbie[/eluser]
I have a CI application which I want to run side by side with WordPress. CI will handle the core features of the application; WordPress will handle the simple pages (e.g. informational, etc.).

I don't want all the WordPress pages access through it's own subdomain or directory. I want the integration to appear seamless. So, I want something like the following:

www.domain.com/ (CI handles this)
www.domain.com/my-app/ (CI handles this)
www.domain.com/privacy/ (WordPress handles this)
www.domain.com/about/person-1/ (WordPress handles this)

The WordPress pages were working until I deployed my CI application to the same server. Now, when I try to access the WordPress pages, I get CI's 404 page.

How do I handle this?