Wikipedia describes firmware like this:
In electronic systems and computing, firmware is a term often used to
denote the fixed, usually rather small, programs and/or data
structures that internally control various electronic devices.
Wikipedia describes the major layers of iOS like this:
In iOS, there are four abstraction layers: the Core OS layer, the Core
Services layer, the Media layer, and the Cocoa Touch layer.
There's a site called theiphonewiki, and its firmware page links to what appear to be complete .ipsw images including all of the software for a given iOS release. So, theiphonewiki considers firmware to be all of the software.
After reading the Wikipedia definition, I consider the firmware of iOS to reside entirely within the Core OS layer, and consisting of the operating system kernel, device drivers, and other hardware-facing software components. Without knowing exactly how iOS is implemented, I can only speculate that these components are clearly defined and distinct (although this is not always the case in practice).
Edit: This TUAW article indicates that all non-bundled applications and user data is erased from the phone during a DFU restore. This suggests to me that the internal storage is completely erased, and all of the device software is reinstalled (low-level operating system, baseband if applicable, and bundled iOS applications).