However what happens if I want to read multiple bz2 files instead of 1 bz2 file?

You should just be able to put the code you showed in a loop, for example my @files = ("debug.log.bz2", "debug2.log.bz2", ...); for my $filename (@files) { my $fh = ... }.

Update: If you're the same anonymous poster, then you seem to have already figured that out here. You might want to consider registering an account so that your threads can be more easily connected, and so that you can edit your posts instead of making multiple anonymous "update" posts. Even if you already have an account you can still register a second one for use at work as long as you observe the Site Rules Governing User Accounts.