hello, Good on ya, guy. You will be happy, I've built several semi underground structures and i have some hints from the experience that you may find useful. While u still have that back hoe handy, have him dig a corner out to an area away from the pit so any water that gets down there has a place to go, or your looking at later having a solar powered sump pump to keep your chickens dry. When u build your walls with whatever you use. Make sure to use some 4 mil plastic around the outside before you back fill. I also use those 2 foot high by 4 inch x 8 foot sheets of insulation ( 2 thick) around the top two foot of the back fill so the frost line is hampered a bit during the winter. It works well.
You will be happy with your underground coop, as the earth is constantly above freezing.
adding a propane light , will keep the entire place heated suitably. When i make a sod roof, i always start out with plastic or the best is Grace snow and ice shield for a permanent water tight roof, then i put sheet metal on it and small rock 3/4 then a small galvanized screen to keep the dirt out of the rock, then the sod. Then i collect all the excess rain water thru gutters off the sheet metal and run it to a collection barrell and use it for the water system for the chickens. Beats hauling the water and i bury the water barrel and the earth keeps it from freezing also.
Your underground coop is a Great idea, it will serve you well for many years. good luck
Doug