For entry into TurboTax, you'll need to split the Form 1099-R into two, one for the portion rolled over to the designated Roth account in the 403(b) and another for the portion rolled over to the Roth IRA. The only difference in the way TurboTax treats these separately reported rollovers is the recording on the IRA Information Worksheet of the Roth IRA conversion basis resulting from the rollover to the Roth IRA.
(Regarding TurboTax being a work-in-progress, splitting of the Form 1099-R under these circumstances has been necessary since 2008 when rolling over a distribution from a traditional account in a qualified retirement plan directly to a Roth IRA became permissible, so this aspect has been a "work-in-progress" for more than 10 years.)
