J.N.
The best way to break your son of this habit seems drastic, but even Super Nanny agrees. Every time you go in to your son, you are giving him positive reinforcement that crying gets attention. The only way to not give him that attention and therefore break this habit is to ignore the crying and allow him to settle back to sleep on his own. I know this can be very hard on a mother, but in the long run, you'll have success. It will take a few nights, but before a week is up, I think he'll be doing much better. Don't be surprised if for the first couple of nights his crying seems worse or lasts longer. He will be testing you to see what will bring you to his side. Don't give in.
As for your husband, his tiredness probably has a lot to do with sleep deprivation. Many people can't function well at all without sleep and become very irritable when sleep deprived. I suggest ear plugs for your husband until your son sleeps through the night, that way he'll hopefully sleep uninterrupted as your son learns to sleep through as well.