A method and apparatus for packaging a semiconductor die with an interposer substrate. A semiconductor device assembly includes a conductively bumped semiconductor die and an interposer substrate having multiple recesses formed therein. The semiconductor die is mounted to the interposer substrate with the conductive bumps disposed in the multiple recesses so that an active surface of the semiconductor die is directly mounted to a facing surface of the interposer substrate. One or more openings may be provided in an opposing surface of the interposer substrate which extends to the multiple recesses and the conductive bumps disposed therein and dielectric filler material may be introduced through the one or more openings into the recesses.