When searching in JEI the barrel and related upgrades can not be found. The barrel card does show however. You can also access the barrel crafting recipe by searching for uses of a log or a slab.

Barrels also lose their type when broken. If you craft a willow barrel and break it you will get an oak barrel.

This is with Charset 1.9.4-0.3.0-Pre7

95efbc3 for the second one; could not reproduce the JEI issue, perhaps I fixed it already?