I don't wear briefs, but I do wear thin snug-fitting midlength coolmax shorts under my cycling shorts for my daily commuting. I feel like this extra layer protects the expensive shorts from body oil and grime so I can wear them 3-4 times before washing. As long as I hang them for throrough drying between uses they never develop an odor. Despite their snug fit these shorts seem may have caused some chafing on a longer ride of 50 miles so I don't wear them for long rides, just daily commuting rides that range from 9 to 25 miles.

I also wear coolmax t-shirts under my jerseys partly for the same reason, but also because is is just more comfortable even in our disgustingly hot and humid weather.
FWIW,
Raymond