My husband sleeps through the baby cries

I've mentioned my concerns to my husband about him sleeping and holding our baby. She's 5 weeks right now but a few weeks ago he fell asleep with her on the couch. That happened a few times especially since he just recently switched to night shifts at work. He said it was because I was in the room he felt safe. Today, I was folding baby clothes on the nursery and heard our daughter crying (I laid her in her bassinet so I thought she'd be ok and he was awake in the other room with her). In a few seconds her crying turned into shrieking and I jumped up to see what was going on and she's lying next to him coughing with puke all over her face and he's snoring right through it. I feel really frustrated that he simply ignores my concerns and tells me not to worry. I'm starting to feel like I can't trust him in the sense that he will literally sleep through anything. There have been several times where I threw pillows at him and yelled while he slept and he didn't budge. I tried making him set up a Doctors appointment to test for sleep apnea but he just brushes it off. What can I do!? I'm really frustrated and it's kicking up my anxiety.