Yes, you can breed them. Having different moms increases genetic diversity but also makes dad more prepotent. It's very common in the horse world, esp. Arabians, to breed half-siblings.
I would if the sire is something you want to perpetuate (ie his dam was a great milker, he has good conformation, fast growth). And for a lot of people, this is the only option they have.
If you decide to breed the kids together make sure their sire doesn't have any major faults. Breeding half siblings will accentuate both the good and the bad. Do your homework on the pedigree to make sure you know what's behind dad.
I happen to really like doing half sibling crosses but I do a ton of research before I do any breeding. We did one this year that produced one of the best kids we've ever had. The sire of both parents is a National Champion that I have used many times and I know what he produces.