If you do not have the humanure handbook I would suggest purchasing it as it would clear up any questions or concerns you might have.
http://humanurehandbook.com/
A well built compost pile will have a huge amount of carbon able to soak up gallons of liquids and prevent runoff. I have heard of people throwing a tarp over their piles during really heavy rains, but in general, a decent biological sponge located in the bottom of the pile will prevent any moisture from running out of the pile. This might include a few broken bales of straw, a big pile of weeds, or bags of raked leaves. If you are still concerned about moisture, simply mount a roof over the pile and collect the rain runoff for cleaning your buckets or directing it straight into your garden. In most cases, the rain will only saturate the pile and make it hotter for better decomposition. A dry pile will not get hot and will need much more time to break down. Cover material is the most important part of humanure, it will help soak up un-needed moisture. Good luck.