Linda, first, so sorry for this.
Second, I have experience with bad bosses, and I can tell you that you never make progress by complaining about how bad the boss is -- that sounds like you're whining and forces the bigger boss to decide who is telling the truth, and that decision almost always goes to the person who has the big boss' direct ear. And unfortunately, it is always the best employees who are the most hurt, because they are the ones willing to go above and beyond to get the job done -- and the bad bosses will take maximum advantage of that willingness for as long as they can.
So you do two things. First, internally, your DH has to redefine his job as "do the best I can for 40 hrs/week," not "get everything done no matter the cost." He is being taken advantage of, and the bad boss will continue to do so for as long as your DH lets him get away with it.
Second, instead of attacking with vague, broad claims like how bad a manager your boss is and how you don't have the resources you need, you manage your boss in a way that demonstrates that the problem is his "management" style, not your lack of effort, along the lines of what MayDay suggested. I.e.:
Every Friday (or Monday first thing), prepare a work plan for the team for the week -- your DH lists his top priorities and identifies the work that can reasonably be done on those priorities in 40 hrs by each available team member. He then sends this to the bad boss, framed up as his understanding of the tasks/deadlines/priorities, and asks his boss to let him know if the boss would prefer different priorities. If they discuss this in person, he should follow up with an email laying out the complete schedule.
Because the boss is lazy, the boss may well ignore this, and your DH is good to go! But if the boss responds that "everything" needs to be done, then your DH revises the schedule to add some work on the projects your boss wants to include and then pushes the due dates back on everything else. Rinse, repeat: send it to the boss as his understanding based on their subsequent discussion, and ask him again to let him know if the boss wants any further changes.
If the boss again responds saying, no, it all needs to get done, the next response is that ok, doing that will require XX more man-hours (if he can break it down by project/task, that would be great), which will require YY more people, and does he have authorization to hire those additional people? And until he can find those people and bring them onboard, which of the first two options would the boss prefer? The ultimate point is to always, always provide the boss options -- but all of those options are "things that can be done in 40 hrs/wk."
As the team is working over the course of the week, if additional work comes in, each new task should be handled by revising the existing schedule to accommodate the new work -- not by adding more hours in the day, but by pushing other work back. That again goes to the bad boss, and you repeat the process -- this should all be phrased as "here is my plan, please let me know if you would prefer me to handle this in some other way." Then at the end of the week, he wraps things up with another email summarizing everything that was completed according to the plan.
Of course, the shit is going to hit the fan at some point, because bad boss keeps bringing in more work than they can manage. But that's ok! Because when that happens, and the bad boss starts yelling at him about why didn't he do XYZ on project ABC, your DH can just look befuddled and say that he was only working on the priorities and schedule that the bad boss approved (and present the schedule to back it up).
The key here is that he is (1) setting the expectations for himself and his team at a manageable level, (2) demonstrating his own professionalism (calmy focusing on getting the job done and making sure his team's efforts are aligned with corporate priorities), while (3) creating an excellent paper trail of facts that point directly to his boss as the problem here (which is both his own best defense and the necessary first step to getting the bad boss fired -- again, management is not going to fire his boss because someone whines he doesn't have enough resources; but if you have a lovely paper trail showing you executed perfectly on the plan that your boss approved, you are giving the big boss the documentation he needs to fire the bad boss). That way, if things come to a head, he doesn't need to argue, or get upset, or be emotionally involved at all: the documents speak for themselves.