When someone gets shin splints what happens is the layer of tissue that is attached to the bone is ripped off due to overuse or wrong use of the anterior tibial muscle (the one right on your shin).
So the worst part about this is that this muscle pulls on that tibia everytime you take a step. The key to quick recovery is A LOT of icing and mobilization. The longer you wait for it to heal the faster it will...sound contridictory '"longer=faster". But really,
Say your husband doesnt run for 4 weeks, minimizes any walking to the minimum, he will ulimetely heal better and will be able to then run for longer of period of time before his chances of getting shin splints again, come back.
As opposed to he waits for 1 week, takes lots of meds, goes running worsens the condition, they he will have to stay immobilized for even longer.
So again, i suggest lots of icing on the shins themselves, and take ibuprophen if pain is unbarrable, but dont take so many that he wouldnt know if the shins really healed or did he just shut off the pain receptors.
And to prevent this from happening i would definerely follow g8r80 and get some custom orthopedics...or figure out what caused the shin splints (another cause could be running downhill) and to never do that action again.
I hope that helps. I know how much this sucks.

Let me know if you have anymore questions.