Starting from version 5.0 RIATest supports automation of HTML pages. You can use this new functionality to automate HTML parts of your mixed application.
From version 4.0 on RIATest supports automation of any Windows application (including browsers) via UI Automation API. You can use this new functionality to automate non-Flex and non-HTML parts of your mixed/hybrid application. For a sample usage of Windows automation in RIATest see Handling Windows dialogs.