I came across a very similar situation when designing the navigation for the application I'm working on. We evaluated several different types of navigation patterns and landed on two when we got into thorough user testing:
The standard hub-and-spoke pattern (when drilling in, the menu button goes away and you must navigate all the way back to the beginning to access the menu again)
The pattern mentioned by previous answerer Neo: the menu button is always accessible, and if the back button appears, it is to the left of the menu button, so the menu button slides over to the right.
You can find a great working reference for #2 in the ABC News app for iOS (go download the app if possible, all of the screenshots I saw via a google search were out-of-date).
We evaluated both approaches and our users much preferred #2, as they were frequently apt to drill into many pages and not want to drill back through to find the menu again.