Look for a brand name (Not Walmart or Sears, etc) bike from your local bike shop (Again, not Walmart, etc). Your best bet will likely be a chromoly hard tail Mountain Bike. Mountain bikes are built tough so the weight shouldnt be an issue... I go about 270 in all my gear and have hit 10 foot drops on an aluminum hardtail so that'll give you an idea of the impacts a solid MTB can take. 300lbs riding around town and on some trails wont hurt anything on a good MTB, plus it'll give your husband a wide range of gearing options to use while riding and working up his fitness.
Brands like Trek, Specialized, Kona, Rocky Mountain, Santa Cruz... Any of the "real" brands should do you fine, just make sure its not a cheap department store bike and he'll be just fine... and ripping up some trails in no time, lol.
Good Luck!