Check out your transfer station, lots of free stuff. Mine has a recycling area (where I found what I needed for nesting boxes), a wood pile, a metal pile, a concrete/brick pile (that I'll be sorting through this summer to build walkways around the coop), a construction pile. The guys who work there are usually very helpful if you tell them what you're looking for. One guy saved me a brand new Harvey window that someone had thrown out. You could even find old doors. I'd definitely think about starting out with fewer chickens as well, easier on the budget feed wise.

Don't give up. You're as entitled to YOUR hobbies as your husband is to his--especially one that comes with so many perks like chickens do. Hey!...without even knowing it, your husband could be providing you with one ready-made coop wall.
If you build your coop using the outside back wall of his shed as one wall of your coop? Hey, remind him marriage IS compromise, and you're a lot more snuggly than a bandsaw is! lol