Anyone have exprience with sonic testing multi layers? As an example, if you have a sleeve in a bore, will it show the sum of the two materials, or does it read only the sleeve?

It will only read the sleeve

That was my understanding also, I suspect however it is measurable, but requires a unit (different?) tuned to a likely much lower frequency so as not to "hear" the "discontinuity", but I bet that gives up accuracy or requires a greater material thickness to measure in the first place.

Been there, done that. It measures the sleeve. Also, since the sleeve is likely a different material than the 'gray cast' block, the readings will be off a little.

Agreed. The discontinuity sends back a reflection. The first use for ultrasonic testing (UT) was to find internal flaws in metal, especially welds.
R.

Can you go in through the cooling passages and measure from that side to the sleeve?

My question was general. Im not actually doing it, just wondering out loud.

You can do it anywhere you can set your probe at right angles resting on bare metal.
There are probes that send the sonic pulse at an angle but they are for finding cracks.

R.