If it is still a problem, I'd see a doc or a physio to get a proper assessment but there are several things that could be happenning.
One is inflamation of the muscle between the two bones in the lower leg and it feels like tiredness or weakness in that area. I think it's called compartment syndrome. I get this when I am coming back after prolonged rest periods and is, I believe, more to do with tired muscles swelling in a confined space.
Another, shin splints, is a new injury to me that I am just starting to enjoy! I am prepping for a half marathon in three weeks and was struck by this two weeks ago. (Might just get there.) This occurred to me as a significant pain on the inside of my shin at the bottom of the bulge of my calf muscle, if that makes sense. I had been running quite a few 8 milers on concrete ( a bad idea I now gather) and this stopped me dead a mile into one of them - I could not run at all. Apparently it's due to over tight muscles pulling on the sheath around the bone causing it to become inflamed.
I believe stress fractures are also a possibility and I hope that neither of us are sufferring from this as this takes months of recovery.
I suspect your husband has the first complaint (he would probably not be able to run with the second or third) and would agree with all the above suggestions. Good running shoes (if it's going to be a frequent thing - get him analysed on a treadmill to select the right shoes), gentle mileage build-up and proper warm ups.
I am a larger chap for a runner (13½ stone) and the weight adds to the stress in the lower legs. It has caused me achillies issues, calf tears and now shin splints. I just have to be aware and take notice when things start to hurt.
Good luck!