Dennis quoted it and added a clarification "electrically joined at both ends "; you don't have both ends of both conductors go to the same place, thus in my opinion, so they are not parallel conductors by the NEC definition. Each conductor goes to its own fuse.
The arrangement you have is safe, as each conductor is protected by its own fuse, but I have no idea if this is code compliant or not. Jim suggests it is not, and I'm inclined to believe him.
This sort of arrangement is used in other jurisdictions, as you can do this to build a safe high availability path (each conductor being adequate for the full load), whilst having the ability to isolate part of it so one can work on it without it being hot. And also needing two breakers or fuses in parallel to both open before the circuit is isolated, making breaker failure not an availability issue. Makes the coordination and fault currents entertaining, if it ever does go wrong, though...