What happens during a flight cycle is the humidity is high during departure, from ambient air and the moisture from the pax, but over time the air dries out because the bleed being supplied to keep the pressure hull "inflated" is coming from the engine compressors, which at 35000 ft has almost no humidity, and what humidity there is is being extracted by the Air Cycle Machines that condition the bleed (by heat exchanger condensate).
It's important to note the air cycle air conditioning process (787 excluded): Take hot high pressure bleed air, take away some of the heat with heat exchangers while keeping the pressure up, boost the pressure and temperature some more with an air cycle machine - more or less a turbocharger that feeds itself - , cool that off some more with more heat exchangers, then finally allow the significantly cooled but still very high pressure air to expand and drop down to just above cabin pressure. This process can take 500F air bleed from the engine compressor and chill it to -40 if you pass all of it through the air cycle machine (only some goes through, and gets mixed with bypassed bleed after, and the air cycle discharge itself is normally kept to not less than > freezing). Anyway, this process takes whatever humidity there is and removes it, leaving bone dry air. Moisture control is a big deal with Air Cycle Machines because condensate water that forms during the cooling process will rapidly erode the ACM turbine and ruin the ACM, so you have water separators that extract moisture that condenses from being chilled.
Then at altitude, there's almost no ambient moisture in the first place and you end up with really dry air from ambient being pumped in, how much depending on how leaky the pressure hull is (they can leak quite a lot) offset by humidity coming from all the pax. At high altitudes after a period of time the dry incoming air wins out and the pax humidity isn't enough and everybody starts to dessicate, again, depending on how leaky the pressure hull is. An older leaky airplane will get a lot drier inside than a newer relatively tight one.
As Mackk says, one of the big issues is that what moisture does get around the cabin ends up condensing on the inside of the pressure hull. It slowly gets absorbed into the insulation. Airliners that operate in humid environments down low will carry hundreds of pounds of water in the cabin insulation because of the condensation cycles from flights, and you will often see insulation set out to dry when airliners are in for heavy check inspections. What water doesn't soak into the insulation collects at the bottom of the fuselage and promotes corrosion (one solution is to pump dry conditioned air directly into the space between the insulation and skin - so called "zonal dryer" systems).
Anyway, you can see there is a this-or-that problem. Air moist enough to keep pax happy plays havoc with the interior. Air dry enough for a happy interior generates dry air complaints. In general, the industry tends to go with the latter.