Lulu,
We do something entirely different:
We travel with one RS rollaboard each and then one small totebag (into which goes my travel purse, our liquids in the baggies, camera, etc.)
My rollaboard has all the folded clothes (t-shirts, socks, undies, back-up shoes, non-liquid toiletries). My spouse's rollaboard contains the hanging clothes and then some folded clothes, too. He loves to wear long-sleeve shirts when he travels, even in the summer, for sun protection.....or flannels for cool weather travel. So, several of his shirts on hangers, an extra pair of trousers, and then whatever of my clothes are needed to put in there in order to have room in the first rollaboard. Then, he puts a light-weight garment bag around all the clothes that are on hangers (think the kind we used to take on board when there was not a one-limit carry on...way back when), then he folds the garment bag into three within the rollaboard. If there is still room in the rollaboard (and there usually is) hats, my skinny jeans, maybe the umbrella, etc. would get stuffed in the bottom or between the layers of the garment bag.
I know it sounds like all that would not fit, but it does. And, it's funny because when people notice my husband is wearing a crisp (appears to be starched shirt) each day, I've had people ask me if I stayed up all night ironing. No, just the ole trusty Brooks Brothers non-iron shirts.
If we have short stays at a hotel of just one or two nights, sometimes the garment bag just gets hung in whole, and I'll just fish out what I need and then hang up the previous day's shirt (he'll the recycle the shirt later in the week...luckily he doesn't sweat much).
But, Lulu, if it is just a couple of shirts that your husband would otherwise hang up, I don't know that it would be worth the whole garment bag thing within the suit case. I'd probably just follow the other posters' suggestions for folding the shirts.
Everyone seems to have a system that works, and you'll come up with what works for you. You've gotten some great suggestions from the others.