In our place, you either get the PH off, or if you work it, it is at double time, but you don't get a day in lieu as well.
I think the bast way of working out his leave entitlement is to convert into hours - as per my example above.
8 months at 30 hours per week (assuming he stays on 30/wk for the rest of the year) = 28 days x 8 (hours) x .75 (30 hrs/week) x .75 (8 months) = 126 hours.
4 months at 20 hours per week. = 28 x 8 (hours) x .5 (20 hours/week) x .25 (4 months) = 28 hours.
So in total your DH is entitled to 154 hours annual leave per year, including public holidays (assuming FT leave entitlement of 28 days per year, the legal minimum).
Rather than looking at how many hours annual leave have been deducted, how many annual leave hours has you DH been paid for?
During the week's leave in February, he should have been paid for 30 hours annual leave, which is then deducted from his allowance. The week in the summer should have been 20 hours.
I'm not completely clear on the public holiday working, as our leave and PHs are not combined, however the logical way of looking at it, is if he works 5 hours on, say, New Year's day, then he deducts 5 hours from his leave allowance, but gets paid 5 hours at double time, so effectively gets paid for his time and also for his leave IYSWIM?