Dehumidifying without an air-conditioner
The humidifier works well in the basement.  Two ideas:


If the humidifier's capacity is adequate and the basement is connected to the HVAC system (vents and a return, and ductwork shared with the main floor), run just the HVAC fan continuously to circulate the house air and let the dehumidifier dry the air for the whole house.
Otherwise, get a second dehumidifier for the upper level.  I see  isherwood commented a similar idea while I was writing this.  If you can set the dehumidifier on a counter next to a sink, you're in business, just like the basement.  If you don't have convenient counter space, you could set up some type of surface next to the sink that is higher than the sink and run a discharge hose into the sink.  If that isn't a good option (sink height is typically higher than normal table height), you can still do it using a condensate pump.

You don't describe the exact setup for getting the water into the drain in the basement.  Dehumidifiers typically have the ability to connect a hose to the collection tray.  Use adapters to connect a piece of vinyl tubing to that tray drain.  

Run that tubing into a condensate pump (http://www.homedepot.com/b/Plumbing-Pumps-Utility-Pumps-Condensate-Removal-Pumps/N-5yc1vZbqoh).  You will need to raise the dehumidifier so the collection tray drain is higher than the input hole in the condensate pump and keep the tubing short enough so it is a straight shot and doesn't dip a lot lower (set the dehumidifier on a small stand or table).  Run the condensate pump discharge to a sink.  

I've done that in an enclosed crawl space connected to a basement and it works well for unattended, long-term use.