I'm using Internet Explorer and Mozilla Firefox. Each for different things. Is it possible to somehow "unify" browsing history from bouth of these browsers so that sites I have visited while on Firefox also would be stored in Explorers history and vice versa?
In short, no.
IE is well integrated to the OS and uses its own temporary folder areas. Firefox is designed to be cross-OS and uses a very different folder structure.
What is more, they both use different file formats.
The only way to do this would be to have an application that trawled through the history folders of each, parsed the data and created its own history list. Possibly, you could do this with something like Microsoft Excel though it would be better done in PowerShell or a scripting language.