I have the exact problem as Dragon with a HE furnace and the humidifier installed on the cool air return, this was installed by professionals 5 years ago, my problem is that assumimg the air flow through the humidifier with the hot air return, then goes down into the J channel to the furnace, since the furnace heats this air, as common sense, would the heat from the furnace evaporate the moisture thus less humidity. As per say if the humidifier did install on the hot air return with the cool air flow through would the hot air then pick up this cool moisture then into the house instead passing through the furnace. Need help with diagrams.

A heating system, if installed properly, is in a loop. Heated air is distributed, cools and is returned to be heated again. It only disappears through leaks. Some people put a humidifier on the cold side since the air is heated uniformly and the vapor is distributed. It either stays in the air or condenses on a cold surface-water on glass windows. When you introduce water vapor on the hot side, the evaporation of the water causes the air ro cool off and drops the temperature in the ductwork. The relative humidity, measured at a central point stays basically the same. The relative humidity on the cold side is higher that the warm side but is blended in the air movement.