If you want to find out what Milton Friedman believed, reading what Rothbard says Milton Friedman believes is not a very sensible tactic, any more than it would be sensible to find out what libertarians believe by reading articles by people hostile to libertarianism. You would be better off reading Friedman.
Monetarism is not a theory about what monetary system should exist but about how money interacts with the economy. One could be a monetarist in favor of central banking, a monetarist in favor of competitive private issuers of money, a monetarist in favor of a gold standard, a monetarist in favor of fiat money. Similarly, identifying with the Austrian school or the Chicago school--or, for that matter, with Keynesianism--doesn't determine one's political views. Someone might believe that Keynes' was correct about macro-economics but that government attempts to use his ideas to control the economy were unworkable for public choice reasons. One can be an Austrian and in favor of quite a lot of government—consider Mises' views on conscription, military spending, and state opera--or a Chicago school anarchist, as I am. There's at least one edition of _The Road to Serfdom)_ that has, on the back cover, a glowing endorsement by Keynes.