Boyfriend has separation anxiety?

My boyfriend has admitted to having separation anxiety and it seems to be stronger when it comes to me. I asked him about it and he said he feels it strongest towards me. When he has to leave me he gets really irritable, agitated, and slowly gets depressed. When he's not with me he complains of a feeling like there is a literal hole in his chest and difficulty breathing. At nighttime he has issues falling asleep and breathing and when he does sleep he has recurring nightmares of losing me. I've had to call him late at night because his anxiety is so bad that only the sound of my voice will calm him down. He won't tell his parents because he says they won't take it seriously or they'll make fun of him. Is there something I can do to help him?