Here is the documentation for the reporting service. http://wiki.collectionspace.org/display/collectionspace/Reporting+Servic...
I am still finishing up some of this (the search filtering by context), and will check in the rest of the code changes today, but the payloads as documented are correct.
Note that while batch jobs are probably not on your radar, the invocation model for them is largely the same. The main difference is that a report returns the actual report, while the batch job can return information about what it did (e.g., creating a new object).
Later (1.12? Post 2.0? - not sure), we will make both of them run async and each will return information about the async "job".