I've just checked this with 2010, Firefox and IE … in all combinations, the highlight in Word stays fixed even if I also click and highlight a word in the web browser. I'm not sure it has to be a Word question, irritating though it is.

Still … if we assume that in your case click'n'highlight isn't stable, you could consider using a character style that includes a background colour: assign a keyboard shortcut to the style, and use ctrl+space to clear it. That ought to be quicker than using the menu to apply and remove highlighting. You could do the same with something harmless such as bold or italic, if that's enough to stand out.