You will not ever have more than one root-logger, so your question is a bit misleading. What you are looking for is how to fine-tune which events each of the appenders does log.
And for that, you add a ThresholdFilter to each of the appenders:
http://logback.qos.ch/manual/filters.html#thresholdFilter
<filter class="ch.qos.logback.classic.filter.ThresholdFilter">
<level>INFO</level>
</filter>
Configure level INFO for the FILE-appender and DEBUG for STDOUT.
Edit: I have to dispute the other answer’s charge that this one is wrong: Yes, you can have more than one root-element in the configuration. That does not create more than one root-logger though, which was what the question’s title asks for. Also, the logback manual states under http://logback.qos.ch/manual/configuration.html#syntax (highlighting mine):
Nevertheless, the very basic structure of the configuration file can
be described as, < configuration > element, followed by zero or more
< appender > elements, followed by zero or more < logger > elements,
followed by at most one < root > element.
It might work, but at the very least it’s against convention.