The waste water backs up into the dis...

Dishwasher manufacturers recommend a syphon break be fitted - but usually there is not a problem if your sink has an overflow pipe incorporated.

You have a partially blocked drain - causing wastewater to flow into the dishwasher instead.

Use 1/2 a cup of caustic soda or proprietary drain cleaner down the sink drain. Add about a pint of water, and leave overnight.
Next morning pour a full boiling kettle down the drain which should move things on and clear the drain.
You may have to repeat this process once, but is preferable to taking your pipework apart - which is next if this does not clear it.