Whirlpool dishwasher will not drain if tub is full

I have a Whirlpool dishwasher that has suddenly stopped draining at the end of the cycle. If I manually drain (with shop vac) approximately 1/2 of the water out of the tub, and run a drain cycle, the rest of the water will pump out fine. But if the tub is full, as is the case after a full wash cycle, it won't drain at all. I can't find any signs of blockage, and water drains freely from both the drain hose and check valve when I separate the two. Any ideas?