Apparently the BD-390 doesn't officially support the DVD-audio format (a big plus for the competing Oppo BDP-83, which also adds SACD support). However, I own two DVD-Audio discs ('Audio' by Blue Man Group and 'The Bluegrass Sessions' by Bela Fleck), and they seem to play fine on my BD-390 (with full 5.1 being sent to my Onkyo TX-SR876 receiver).
So does this player actually support DVD audio? Or was I just fortunate to test two DVD-audio discs that were encoded in a way that the BD-390 could read?
EDIT-Some more research revealed that most DVD-Audio discs have Dolby Digital and/or DTS tracks included, so that standard DVD players can decode them. The BD-390 just can't decode the uncompressed MLP tracks on DVD-audio discs. Bummer!