I think in the end we develop our own way of talking at even a personal level. I say the half part, and the half but others might consider this snobby or dialect or something else wrong... Duolingo does its best really. Nothing is entirely correct in life. Ha det på badet.
This is my guess:
I have A whole loaf of bread = Jeg har et helt brød
I have THE two whole loaves of bread = Jeg har de to hele brødene
From what I have learned so far, you'd also need the "det" in your first sentence:
I have THE whole loaf of bread = Jeg har det hele brødet.