You sound like a very good neighbor, & hopefully your neighbors are good too, just very naive. But if your neighbors say they dont want their dogs to hurt your chickens yet continually allow their dogs access, their (in)actions speak louder than their words. And based on your descriptions, the dogs Will kill your chickens; its a matter of when not if. And sadly it sounds like your husband may not greatly value the lives of your flock members either? Dont simply rely on your husbands stance, Call animal control yourself, and learn your local ordinances and your rights. Hopefully after you know your rights, your husband will be willing to back you up.
Hardware cloth dug 3 feet down or an apron 3 feet out and attached firmly to strong supports should work. Its not your responsibility to keep the neighbors dogs out of Your yard, but they wont take action you may have to. If practical, electric fence running the length of the gap may be your best solution of all.