Definitely DO NOT use regular water in an ultrasonic humidifier, only distilled. Apparently the ultrasonic element makes it easier to inhale the minerals from regular tap water, even the best, softest tap water will have minerals. You can confirm this by seeing a white dust on your furniture, imagine what it's doing to your lungs. I wouldn't even use my humidifier if I didn't have distilled, I guess I'd use a regular wick type.
Those integrated home humidifiers aren't worth it. They barely raise the humidity by 1-2% and are just a horrible place for mold to grow.
As a side note, I knew someone who worked at a chip factory, where the purest water was required for the fabs, it was basically 100% H2O. I was told you could die if you drank it because it would draw out all of the sodium / electrolytes you need to function. Not sure if they were pulling my chain or not.