That's actually how I've worked my lifting schedule for a few years now. I started doing it when I was following Wiggy's Singles & Doubles, then continued doing it when I started doing 531, and still do it with Juggernaut now. Only difference is I superset a pull before each push on my main lifts, so:
A. Row (different variations as I feel like changing it up)
-Military Press day
A. Weighted pullups
B. Military Press
I've been doing it so long, I hate doing it any other way at this point.