My fence is 6' high (with a roof of wire) and I've seen a couple of my birds fly right up to the top. I'm sure if I didn't have the wire roof, they could have gotten out. That large run your husband is making looks nice for your birds, but without some type of top, it will make a great runway for birds of prey to swoop right down and grab a chicken meal. You don't necessarily need a solid roof, but at least something at intervals to break their flight pattern.
chickens will roost on the edge of the wire, then drop to the outside area. if you do not use a roof, run a fence at least 4' feet, but give them some roost areas in the center (not near the edges). I started small too ($$$), but then went to a 6' horse fence with a plastic bird netting. I had to cover a 100x100 area. I was not concerned about predators, except hawks. If $$$ is not a concern, go all over wire.