I'm all for some degree of neatness (not perfection!), because I feel better and can be more productive when there isn't total chaos. I wonder if your husband is like that, too. Our house doesn't look like a magazine article or an HGTV program but, if I take a little time to establish/reestablish a little order, I actually have more energy for things.
Right now I have clutter all over this desk, a project is on the table, the ironing (yes, I do that) isn't finished yet, and the laundry room is a disaster area, to give just a few examples. But I have made the sitting areas easy to sit in, the laundry is by the washer instead of on the family room floor, the residue from eating and drinking has all been taken to the kitchen, and I know I'm putting a few minutes in on the rest of the laundry room tomorrow. I know which few minutes they'll be, too, unless tomorrow's schedule goes crazy.
You may need to schedule clean-up just the way you do your many other family activities. It's amazing what picking-up can be done in just fifteen minutes, or even five.... especially if you can set a timer and make a game of it, which is what I do when my granddaughters visit, or do for myself when my granddaughters aren't visiting.
It wouldn't be too much hardship for your family to abide by a few basic rules - such as: "The jackets you take off when you come in the house you hang on the hangers and you don't dump on the floor." Or: "Backpacks and schoolbooks are put HERE, not left all over the house." Or: "What you eat and drink in your room you clean up *immediately* after you've eaten and drunk." That's not too hard. Busy people - even lazy people, which your family doesn't seem to have - can handle things like this.
By the same token, you need to schedule regular goof-off times, veg times, whatever you want to call it, so that people can put their feet up and read a book or play a game if that's what they want to do. Everybody *needs* that kind of time, and it's better to arrange it than have to steal it.
This is a non-battle, unless you and your husband want to make it one. Homes are messy because life is messy, but the mess can be controlled enough so that everyone feels comfortable. It may have to start with you since you wrote this post - unless there's a "Papapedia" site your husband is writing on! Is there one area which would make him really, really happy if it were maintained better? Why not give him a present of it? That might help him to relax when it's relaxing time. And it might help you relax because he's not after you about cleaning up.
(P.S. I like Fly Lady, too.)