Sounds like food particles. First check the inside for any remaining food that didn't go through the filter and if you have a removable filter make sure its clean.
You may want to check the discharge hose. Take it off and run some water through it. And lastly check your disposal units connection and make sure you've run enough water through to clear away any material in it.
The other side of the issue is the water supply: If you have a well you maybe getting sand in the water check your well pump and water tank.
You may want to install a grit filter in the main water line even if the water is supplied by the city or town.
Run the dishwater with no dishes to hopefully finish flushing any stuff out of the lines.