Common wisdom says don't paint the inside. This was probably good advice when the only paint we had was made with Lead. Since Latex -paint was invented a long time later, no one every tried it on the inside.
However, if you coat the inside with Latex, the SHB hate it. They will not lay their eggs in Latex painted wood. I had 7 hives painted and the bees could not have cared less. They will live in steel drums, old cars, clay pots, plastic water meter boxes, out in the open on tree limbs, etc. I live in SW Florida and SHB are a very real problem. My seven hives did very well for the two months I had them in painted boxes. Then a bear got them.
The SHB also hate light, so if you put a translucent top cover on the hive, throw away the inner cover and put on a screened bottom board, you will have eliminated 90 % of the places they can lay their eggs. The only place left is in the comb and the bees are all over that.
BTW the paint was not my idea originally, it comes from a friend of mine who is head of the ethomolgy dept at a large univer sity on the Left Coast.