Kitchen Large Electric Appliances - Dishwasher is draining through top of sink

My Kenmore dishwasher is draining the water out through the valve on the top of my sink to the right of my faucet. Should this be doing this, becuse this dirty dishwater is then running into my sink. Any suggestions?

You have plug in either the chrome 'air gap' (there is a baffle inside), or in the rubber tube that is between it and the drain that it ties into (but I doubt the problem is in it on it's own accord), or the "y" part of the drain where there is a baffle also inside that often gets goobered up with gunk. I would start with that last piece mentioned, as it is the easiest to get to and to remove and clean it out. It is a "y" type tail piece section of the drain that you can remove and clean.