For my applications, we purchase lamination stock which already has a coating on both sides of the laminations. We use two different methods to make our cores:
1. Stack laminations to the desired thickness, then cure in an oven at rather high temperatures while the stack is in compression. Once done, the shape of the final core can be either machined, or wire EDM'd.
2. Stamp the individual laminations to the final shape, then stack and cure them in the oven. Then, if accuracy is required, further EDM can be done.
But both cases require high temperature. I suspect that interleaving the E/I's through the bobbin, then curing it, may be too much for the bobbin to handle, or even the insulation of the wire. So I suspect most of the cores out there will not be interleaved, especially if they don't want lamination noise.
edit...ah, I didn't consider varnish impregnation of the entire core as well...my app, the varnish would not survive the x-rays.....AndrewE, Andrew T... nice comments..
jn