I think that as it builds uber, its heal targets gain speed up to 10% faster speed based on uber amount, and the medic moves as fast as they do.
+medic and heal target have 5% resistance to all damage
-100% slower uber build rate, but 50% slower build rate if heal target is already overhealed,regardless if it is match setup time or not

During uber, Medic and heal target gain 50% speed bonus that stacks with the 10% bonus based on uber, but the 10% goes down as ubercharge decreases during uber. Only afterburn, explosions(not rockets or grenades direct hits though), fall damage, out of map death boundaries(such as the cliff of high tower), and all other non direct damage can harm the medic and heal target during uber. Movement impairing effects do work, but only half of their normal impairments. For example, natascha shooting you would only slow you down half as much as it normally does. Medic and heal target can also walk through enemies and enemy buildings, but they cannot perform any objectives while ubered.