When you say two things in the same breath, you say them at the same time. You might apologize for being late and in the same breath criticize the driving directions you were given.
In the same breath is a great way to say "at once," or "at the exact same time." In practice, it really means "more or less at the same time," since it's physically impossible to say two things at once. It's fairly common to use this phrase when someone is expressing conflicting opinions or feelings at the same time, as when you beg to be invited to a party and, in the same breath, say you don't really care if you get an invitation or not.