At the annual Society of Biblical Literature meeting in San Francisco, I and a number of other folks picked up John Schwandt’s audio version of the United Bible Societies’ Greek New Testament (4th ed.; affiliate disclosure).
An audio version of the Hebrew Bible is also available here in “Sephardic-style modern Hebrew.” Although the audio quality is not as crisp as it is for Schwandt’s GNT recording, these Hebrew Bible recordings are an excellent, free resource. They seem to follow BHS (5th ed.) (affiliate disclosure), but I have not seen this fact explicitly stated on the site.
When you “right” click (or the equivalent for your operating system) some blank space on the page, the context menu should display a DownThemAll!… option. Clicking this option should display a dialog box in which all of the page’s individual, chapter-by-chapter mp3 recordings are preselected for download. Clicking Start! will then let this download run in the background while you do other things rather than requiring you to click individually on each chapter’s mp3 in order to download it.