tunnels are very error-prone and even when you place them correctly in the map editor, they are STILL not going to work correctly ingame. It's a pain, I know... But I'll explain how to correctly place the tunnels and how to fix the tubes afterward.
First off, it's best you enable marble madness mode before you draw the tubes. You'll then notice spiral looking thingies on the sides of the bridges. Now select 'Create tunnel' on the sidebar, place the mouse cursor over a spiral thingy on the side of the bridge, click and hold the mouse button and then drag the mouse cursor to the spiral thingy on exactly the opposite side of the bridge, after which you release the mouse button. Repeat this process to connect all of the oposite spirals along the entire length of the bridge and you always only have to draw into a single direction. Take in mind that you can never draw more than 64 tunnels on a map.
Now this is done, save the map and open your map in wordpad. The first thing you need to do now is disabling word wrap. To do this click 'View' at the top of the window, go to 'Options', select 'No wrap' and finally click OK.
Now scroll all the way down until you see [Tubes]. Under it you will see many lines that look similar to this (I removed a lot of -1s at the end of all lines to properly fit the lines below one another on this page):

0=138,133,0,138,130,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
1=138,130,4,138,133,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
2=139,133,0,139,130,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
3=139,130,4,139,133,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
4=140,133,0,140,130,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
5=140,130,4,140,133,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...

Every line is a tube; a tube always goes into 1 specific direction, meaning 2 tubes together make a single tunnel (with only a single tube, units would only be able to enter a tunnel from one side). So 0 and 1 make 1 tunnel, 2 and 3, 4 and 5...
So the problem is that the map editor always makes the tube for one specific direction shorter than the tunnel actually is and this will cause units to either be unable to enter the tunnel or the units will have no image when they exit the tunnel. It's always the tube of the lines with an even number that are broken, so the tubes that will need to be fixed are lines 0, 2, 4 and so on.
So in order to fix the tubes you simply need to replace the first '-1' of all broken lines with the number that comes before it. So after fixing it, the tubes will look like this:

0=138,133,0,138,130,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
1=138,130,4,138,133,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
2=139,133,0,139,130,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
3=139,130,4,139,133,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
4=140,133,0,140,130,0,0,0,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...
5=140,130,4,140,133,4,4,4,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1...

And that's it. Now there should no longer be any problems when units pass under bridges on your map, provided your map doesn't have more than 64 tunnels (that means 128 tubes)