This is a really tricky one.
It sounds like your DH has got used to being your PiL's ... I was going to say carer, which isn't quite right, but support. It's normal for him to talk to them and listen to them, and with this recent tragedy, that's become a part of his life.
I'm going to guess that in usual circumstances, you don't need that much support. You aren't a wife who expects to be called repeated times a day, and that's the pattern your relationship has fallen into, and in usual times, you're okay with that.
The problem is, these aren't usual times. You have a new baby. More than that, you have post-natal insomnia and a baby that doesn't sleep.
I think DM's (if they're the primary carers), tend to bear the brunt of baby care when they're new, and DF's, no matter how empathetic they are, can't really appreciate what it's like to be severely sleep-deprived, with a baby who won't let you put it down and no chance to even drink a cup of coffee. It is absolutely exhausting and debilitating.
I think you are being a bit U, but actually I think you have every right to be. Extreme sleep deprivation gives you the same rights labour does - you are allowed to yell at your partner about stupid stuff, and his job is to give you a hug, take the baby, and walk it around the block while you calm down. If he wants to call his parents at the same time as he's walking, fair dos.
I think the problem isn't the phone calls - the problem is that you and your DC need a lot of support at the moment, and you don't feel like you're getting it.
You don't say how old your baby is, but now he's a dad, your DH's responsibilities have changed and he needs to step up.
I do also agree with PPs that he has a responsibility to his grieving parents though. Would it be possible to get a bit of extra help? Perhaps a sleep doula for a week (worked wonders for a friend of mine). Or your mum to stay or a childminder for a couple of afternoons or something? My DH's solution when we're holding too much is always to get extra support, and it usually drives me mad because I want HIM to help, but he's usually right.

, OP. Sleep deprivation is a special kind of hell.