Is my china covered if the mover breaks it?

It depends on who packed the china. If you packed it, then you assume responsibility for any damage. If you have paid for breakage insurance as part of your moving costs, then you need to check the fine print. If items you have packed are covered, then you can make a claim from your mover.

If the mover packed the china, then the mover should be covering any damage either out of pocket, or through their own insurance policy. If the mover declines to pay the cost to repair or replace, then you can make a claim. What will usually happen, is that the insurance company will pay you, less your deductible. Then the insurer will likely attempt to gain back the paid out amount from the mover. If this is accomplished, then you likely will get back your deductible.

This is another instance where having documents showing the appraised value of the china or a sales receipt would be very useful in the claim process.