I see several questions regarding using h2 database with Jasper Studio. I have the same problem. I have studio version 6.13.0 and h2 build 1.4.200. I can successfully create a data adapter and test it but when I use it in a report there are no tables. I have added the connection parameters AUTO_SERVER=TRUE and MV_STORE=TRUE, but no different.
Ignore this question, I have worked it out, it is a matter of location of the table. In the h2 console the table is shown at the highest level, in Jasper it is under Public/Tables.