WARNING: I'm afraid this message is actually irrelevant. See EDIT note at the end.

Well, you can have your two processes communicate with yet another named pipe. I really think you should (re-)read perlipc. There are lots of examples for this kind of stuff. Check out the open() command for instance. You can use it to fork and create a named pipe in the same time. See the "Safe Pipe Opens" section.

Maybe something like this:

if (my $pid = open(JSON, '|-') {
    # database stuff
    print JSON $json;
} else {
    # this is the child fork.
    # STDIN here is actually JSON in the other fork.
    # network stuff
    my $json = <>;
    # some more network stuff I guess
}
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EDIT I've just realized this wont solve your issue since the child process would block waiting for data from the parent process. It can't do that *AND* act as a network server at the same time. It only moves the blocking problem from one place to an other. So I'm sorry, I don't know.