Adding underlayment between subfloor and vinyl plank flooring

We’re installing vinyl plank flooring. The current problem is a 7/8” height difference between the subfloor and bathroom tile. So, we’re thinking we should lay down 1/2” plywood as underlayment on top of the subfloor to bridge most of this height difference. The subfloor is 3/4” OSB. My questions are: 1. Should we use OSB or plywood as the underlayment on top of the subfloor? 2. How should we fasten the underlayment to the subfloor? 3. Should we add felt paper between the subfloor and underlayment?

Thanks!