I have already drank a half bottle of coffee (today/as of now...)
I have drank a half thermos of coffee. (given the question we don´t need to answer with "already", since it´s implicit from the question, same goes to the above answer).
I have finished a half thermos of coffee. (let´s think there was some coffee in the thermos, say almost half of the thermos capacity, give or take some more.)
This comment takes into account your question, but a native from the UK would answer more in terms of cups: I have drunk n cups of coffee.
I used the British way, since I saw there´s some gramaticall disagreement when it comes to the verb "drink" past form, differente forms used in the different sides of the pound.
Plus, if a native from UK would express that "half" thing, they certainly would use "I must have drunk half a litre of coffee" (certainly a Brazilian in the UK, he hee.)