OP, your story struck a chord with me. My experience is different, but similar.
My mother was so emotional and over the top about difficult situations. She could take someone's problem and make it, not only her own, but much worse. My sisters and I learnt from a young age that we couldn't take any problems, worries or upsets to her as she would take it and run wild with it, crying, worrying, obsessing and literally making herself ill sometimes. And yes, being angry with us for 'causing her problems' or 'making her worry'.
It was so bad that, when I had cancer as an adult, I didn't tell her. My sisters knew, but we had to keep it a secret from her as she would have been in despair, catastrophised, become ill with anxiety. It would have become all about her and how awful she was feeling, when I was the one who was actually going through it.
Luckily, I had my sisters and friends for support, and maybe you will need to look to others, as pp have suggested.
There was no quiet listening, no empathy, no comfort, no advice. We couldn't even rely on her to take our side over things. She was the opposite of a rock. We had to protect her from bad news, problems etc.
Sadly you seem to be in a similar situation with your DH. Some people are obviously just like this. You could try talking to him, explaining that if something bad were to happen to you (eg an accident, serious illness), you wonder how he would react when you told him, and what are you both supposed to do about that? Not tell him? Have to put his emotions and reactions above your own? How that would make you feel, and how he would feel if you felt unable to 'burden' him with something so important?
Sorry if I've gone off on a tangent and you don't feel this relates to your situation.