I logged on as Administrator twice, both times found it already set to custom, explicitly set it to Mozilla Firefox, logged off and re-logged on to my restricted user.
Clicking view e-mail in browser still launches IE8 to view in browser to display the e-mail.
Note that when I click a link within an e-mail, it correctly opens the link in Firefox. The incorrect behavior only occurs when choosing to view an e-mail in a browser.
Also note that the only reason that I am trying to view the e-mail in a browser is that Outlook 2010, unlike Outlook 2003, is not respecting my IE8 setting Tools > Internet Options > Accessibility > Ignore font sizes specified on webpages. If it respected that,
I would have no need for viewing in a browser. But if I am going to view in a browser, I want to use my default browser.
Change the value of (Default) in each of those keys to "C:\Program Files (x86)\Mozilla Firefox\firefox.exe" "%1" (including quotes; if you have 32-bit Windows 8.1, change Program Files (x86) to Program Files).
I also installed unMHT, per mattb5906's post above.
Toa Of Justice — "Only the best is good enough." -Ole Kirk Christiansen, founder of the LEGO Group