A lot of tutorials explain how to set up TimeMachine to make backups of FileVault-ed home directories while logged in, for example here or there.

This little command line tool helps with adding a reference to your home folder to TimeMachine's .plist file (/Library/Preferences/

Execute it as

...> sudo ./include-filevault-volume /Users/myhome

where /Users/myhome is the path to the directory you want TimeMachine to include.