It is actually the opposite. The white will only carry the imbalance of the two circuits of a multi-wire circuit.
For instance, if the black is carrying 10 amps, and the red is carrying 7 amps, the white is only carrying 3 amps.
This is provided the multi-wire circuit is wired correctly. Meaning the two hots are on different "phases" in the panel.
Sometimes I feel like if I answer any more questions it is like someone trying to climb over a fence to jump off a bridge and me giving them a boost.
Answers based on the 2008 & 2011 NEC.
Speedy Petey is right about having the "hot" wires on 2 different phases in the panel. To check this, you should have 240 volts (or close to it) from black to red. If you have nothing from black to red, then both "hots" are from the same phase...and you would be overloading the neutral (white) wire, as you first mentioned. "Edison 3-Wire Circuit"...http://www.bobvila.com/BBS/3_wire-El...l-1-T1593.html