"Your husband is more concerned about the fact that a stranger may think he is jointly responsible for a child having a non-harmful amount of calpol than he is about his wife having an hours sleep in two days whilst looking after sick children.
His self-absorption is breathtaking.
Is this a pattern?"
This
How do the words 'it was my fault and we mis communicated' mean you are trying to blame share?
Why is that his first thought rather than being worried about you or your child? And if being pedantic, if he was in a position to help you in the night and didn't, then he is partially to blame wasn't he? Because if he hadn't been so lazy / selfish, then you wouldn't have been so tired and wouldnt have made a mistake.
Most people at some point do something that accidentally hurts their child. If it was an accident the other parent if they are (both) decent, usually tries to play it down as they know it was an accident rather than negligent and they know the parent that caused it will be feeling really fucking awful already. Only exceptions in my opinion are when one parent has repeatedly asked the other parent to do something that keeps their child safe and it's been ignored. For instance if your husband had asked you a few times already to make a note on a kithcen whiteboard of times of calpol and you hadn't.
Instead your husband is effectively more worried about hammering home 'it's your fault OP, not mine at all!' Rather than trying to check you're actually all right. And unless its completely out of character that makes him a knob.
My husband has a slight tendency to do this eg he will tread on my foot and instead of saying sorry are you ok he will say sorry but you were standing in a stupid place. I tell him it's not on every time, the first thing is to check everyone is ok then apologise if you've hurt someone even if unintentionally and then if I was standing in a stupid place ask me to stand somewhere else next time. Dont apportion blame as an initial reaction.
After a close shave with calpol me and my husband now whatsapp each other with when we gave a dose especially if in the night and the other hasnt woken, just incase, might be something you can tell the safeguarding team you will look to do in he future