Shouldn't be an issue as your Onkyo 605 can decode the DTS HD Master Audio formats so as long as the settings are correct, it should be fine.
Assuming your 350 is connected into the Onkyo with an HDMI cable, let's do a basic check of the settings, as per page 44-45 of the manual, under Audio Settings, have you got Audio Output Priority set to HDMI, Audio (HDMI) set to Auto, BD Audio Setting set to Direct, Dolby Digital set to Dolby Digital and DTS set to DTS?