A good part of my job role is recruitment and HR in a very male-based industry, so here's my take:
I would spectacularly, amazingly far rather a new employee delayed their start by two weeks than either
a) (best next choice) started their job and immediately went off or
b) Just didn't tell me!
Feel free to show him the next bit: 
The half-baked bollocks your DH has going on here would wind me up a treat. 'I'll just take one day and not tell anyone...' is a recipe for making him look a tit, frankly. It doesn't show commitment, it shows panic, and an inability to plan and prioritise. It's applying a strategy of 'oh, shit, er, stick fingers in ears, go la,la,la and pray. Soooo not what's needed in anyone senior.
When our staff do this, it makes me want to sack them on the spot. I can't count how many times I've heard 'oh, my wife's having a baby, no, I didn't tell you cause I'm not planning any time off.' Usually followed by 'What do you mean, what's my plan if it doesn't go smoothly....?'
Even if you do cope, even if he doesn't end up having to make the 3am phone call that inevitably follows the conversation above, it marks his cards. I remember which of our staff did this, and it does not a good impression make!
I'm impressed when staff come to me with things like this, to give myself and the business chance to plan for it. If he tells them now, and better yet, offers suggestions for making it work for all parties, he comes off as mature, balanced, organised and trustworthy. If he hides it, lies about it, omits it, it will cause doubt and resentment.