Depends.

If the airlines have interline luggage agreements, maybe. I had a simple Delta to Montreal round trip connecting to an Air Canada Montreal to Quebec round trip and was told no problem. My originating airport marked the bags through but warned I'd have to clear Canadian customs in Montreal. I did, then Air Canada insisted on retagging luggage before sending it to Quebec. Coming back, we left Quebec 90 miniutes late and missed the Delta connection home. There was a later flight, but by the time I got my luggage I all but missed it.

So good luck. Your 3 hours in ZRH gives you time to do whatever is needed.