The faucet in our kitchen drips or runs when someone is running a bath or taking a shower in the bathroom upstairs above the kitchen. Any ideas? It only does this if the kitchen faucet is on the hot side. If you turn the handle to the cold side, the dripping stops.

Do you know if you have a stem and seat or a cartridge valve on the kitchen faucet?

The kitchen faucet has a cartridge.

Shut off the supply and remove the cartrdige to clean it of debris. If that doesn't help most cartrdiges are guaranteed for life. Moen, Kohlor , PF, etc are all lifetime. Do you know what you brand have

It's Moen.

The Moen site has some great tutorials. Installation Help / Animated Tutorials for Moen Faucet walk around the site and find which cartridge you have and then play that tutorial. If this gets confusing just post back and I can help walk you through it, just make sure your main supply is OFF

You have been very helpful. Thank you for your time :)

You are very welcome. Keep in mind that Moen will ship you a free replacement cartridge if you'd like, also on their site