He should just phone up the school in the morning to say he has diarrhoea and it's kept him up for a few hours. He should then say that his wife is going to the pharmacy when they open (usually 9am) to get medication, and that he really hopes to come to work as soon as they kick in. Your DH can then contact school just before he leaves home (I.e, when he's back in the UK and ready to travel to work), and inform them that he's on his way. Buy a box of tablets and get your DH to take them to school with him too.
Your DH could even tell a half lie, and say that he was at a wedding on the Saturday or Sunday and thinks he must have eaten something dodgy there - I find it's always easier with a half lie.
I've done similar things to what I've suggested above in the past, and have known many colleagues and HOD's do similar.
If your DH has an inset day, then in my experience, he'll be missing next to nothing by missing a couple of hours. If his missing a couple of hours with a tutor group, then obviously it's worse, but teachers are not robots and they do get 'ill.'
I had a friend in one school who was from a different country, and her partner had booked a 7 day break and 3 of these days were days she was meant to be at school. She planned cover work in advance and emailed it in each morning from her holiday - just quick 5 minute emails. She then had a friend who was based in the U.K, but from the same country as her, phone the school each morning pretending to be her! That was very naughty!
One of my HOD's used to feign illness when meetings/twilight sessions etc clashed with certain football matches, and would leave early or have the day off.
My HOD in one school even pulled a sicky on her Birthday - two years in a row, one year it was for one day, the next for 3 days leading to the weekend - If that's not cheeky, then I don't know what is!
I hope those examples have made you feel a bit better. Definitely don't ask the schools permission, they'll get pissed off and probably not let your DH, or get pissed off and reluctantly let him and hold a grudge. Just tell a decent lie, you'll get what you want that way!