If you've got one part in one file and another part in another file, you've got a couple of options. Either one should work, but with stuff like this, there's always a risk that you or the game itself will mess something up and do irreversible damage to your map. Make sure to back it up somewhere before going any further.
a) Put both files in a set as separate diffs and copy the objects in the in-game editor
Make sure the difficulty names are different before adding the file with the other person's part to the mapset folder, otherwise your map will get overwritten, and that's no fun at all.
Once you've got both diffs in the set, you can just open one of them in the editor, copy the objects like normal, press Ctrl+O to switch to the other diff, and paste the objects. You can copy and paste timing points the same way (for sv changes and whatnot). You can hold Ctrl or Shift in the timing panel to select multiple lines at once.
b) Copy the objects in notepad
Just open both .osu files in notepad or any other text editor and copy the lines under [HitObjects] from one file to the other. The objects might end up being in the wrong order, but that shouldn't cause any problems for the editor. The order will get fixed once you save the map in the editor, anyway. You can copy timing points with sv changes this way, too, but you should either know which ones to copy or just get rid of any duplicates later.