OSB subfloor w/ 3/8ths inch plywood
While it addresses the problems with tile on OSB (OSB swells and cracks the grout), it may not tell you conclusively if you need to replace the OSB.
I'd say you'll have to get rid of one or the other.
I hope this helps.
P.S. The number one rule to installing tiles are to have a very strong and sound subfloor.