Is it possible for a child process to inherit a handle from its parent process if one process is 32-bit and the other is 64-bit?
HANDLE is a 64 bit type on Win64 and a 32 bit type on Win32, which suggests that even it were supposed to be possible in all cases, there would be some cases where it would fail: a 64-bit parent process, a 32-bit child process, and a handle that can't be represented in 32 bits.
Or is naming the object the only way for a 32-bit process and a 64-bit process to get a handle for the same object?
If it is a file handle or other kernel handle, then yes.
It just happens that although HANDLE is a 64 bit type, it can always be converted to 32 bit and back for any valid handle value.
GDI handles cannot be inherited.