Can I combine 1/2" and 3/8" plywood for a total of 7/8" subfloor for laying a hardwood floor?
Structurally, there is nothing wrong with your plan.  But I suspect your floor might be prone to squeaking due to having 2 layers of plywood rubbing each other.  Gluing them together will prevent the squeaking.  But gluing large pieces isn't that practical thus a less reliable option would be putting lots of screws to keep the 2 together.

That being said, don't you want to put an underlayment between the plywood and the new flooring?  That serves as a cushion, moisture barrier, and help w/ the sound isolation.  Take that in account.  It is usually 2-3mm thick.

Would 3/4" plywood plus the pad be close enough to your existing floor?