At what point does middle-of-the-night become morning?

This was the topic of discussion last night as Neil and I went to bed.
We take turns getting up with Wes in the mornings, and the deal is that whoever is not getting up in the morning has to get up if Wes wakes in the middle of the night.

It's really a sort of gamble these days, as sometimes Wes wakes up at 5:30 am and sometimes he wakes up at 7:30 am. And when he is up, he's usually up.

For the record, in our household the official time that morning has arrived is 5:30 am.

I won the big prize this morning, as it was my turn to get up, and we had to wake him up at 7:30!