Yes jtbandes, the input language is maintained per application -- in fact per window, because multiple IE browser windows each have their own setting. Windows is known to be very very poor at handling multiple input languages, and can sometimes not even remember the language used inside a single application when switching a lot. I'm Danish, working with English content, on Austrian (German) Windows computers, and I've seen this too often to count.
The best solution I can offer is to choose just one input language and go with that one only.
For me, it means always using a Danish layout because then I can type the German special characters (the DK layout has an
¨ umlaut key) as well as the Danish special characters (which a German layout can't), plus all of the English of course.
The downside may be a suboptimal typing speed in other languages, but at least the keyboard matches Windows' input language all the time. It's very rare that the chosen language actually prevents you from typing what you need.