What is the rock I found on the Delaware river yesterday?
The boulder appears to be dark grey  fossiliferous limestone or dolostone with softer tan layers which might be: limestone or calcareous claystone/siltstone/sandstone.
From the photo, the tan layers do not appear to be shale.

I have a hand specimen which is very similar from southern New Jersey.
It is harder grey limestone inter-layered with light tan calcareous siltstone.