I can't remember any specific instances when Harry knew that he was speaking Parseltongue aside from the one instance in the Chamber of Secrets, where he used it to open the locked door to the chamber.
The following instances are those that I can think of where he does not know that he is speaking Parseltongue:
Sorcerer's Stone - he speaks to the snake in the cage at the zoo.
Chamber of Secrets - he tells Draco's conjured snake not to attack another student.
Deathly Hollows - he speaks with Bathilda Bagshot (who is actually Nagini).
This question arises mostly because of the last item on the list from Deathly Hollows. Nagini did not speak to Harry until Hermione was out of earshot, so that she did not immediately hear them speaking Parseltongue (Hermione would immediately know).
What confuses me is the following: On several occasions, Harry is unconscious of the fact that he is speaking Parseltongue. However, in at least one situation, he consciously uses the language to perform a task. The latter of those make me believe that Harry is able to consciously control his usage of the language, yet in Deathly Hollows, where he seems to have more command over his magical powers, he uses the language unconsciously and it almost gets him killed.
So my question is, particularly: Why does Harry not know, at such an imperative time (Bathilda Bagshot's home), that he is being spoken to in Parseltongue when he demonstrates an ability to consciously control it even in his second year?
PS - Magical languages may be different, but being someone who speaks two languages I find it practically impossible to be unaware of when someone is speaking my second language to me.