I don't think the line chart visual offers this kind of behavior. The closest thing it has is the reference line, but I guess it's not what you're looking for. The best option I can think of at the moment is to create two calculated columns for each column displayed on the line chart, defined as follows:
1. ColNameBelowThreshold = IF([ColName] <= threshold, [ColName], BLANK());
2. ColNameOverThreshold = IF([ColName] > threshold, [ColName], BLANK());
3. threshold can be a variable, a static value, or a calculation of some sort that represents the desired threshold.
4. You might need to tweak the above formulas a bit, depending on your data, so that one line would pick up where the other one ends.
You could then display them both on the line chart, and give ColNameOverThreshold a different color in the "Data Colors" menu in the formatting pane to make it apprear highlighted.