Here are the frameworks I am using:
Runn
If you're not already doing it, you may want to route via Backbone through the hashtag changes (it's his normal behavior, pushState: false), as modifying the hashtag would in no way result in a server call, thus ignoring Codeigniter's router.
In your example, you would want to navigate to localhost/#otherPage.
Then use Codeigniter's router for your ajax REST calls.