Boyfriend has severe social anxiety

My boyfriend has severe social anxiety when we're out in public. For example, we went out to dinner with my parents the other night, and the whole evening he couldn't make direct eye contact with my parents, he kept getting up every five minutes to use the bathroom or refill his drink, and he constantly shakes his leg (like a nervous habit). Then in the car ride home he broke down crying because the evening was too much for him. He's not like this when we're at home alone together, it's only when we go out in public. It's hard to do anything with him, and I'm at the point where I don't even want to ask to go out anymore because I know he'll say yes to please me but it will be torture for him once he's there. Anyone have any advice on how to deal with this?