open adoption

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun The policy, practice, or agreement allowing contact between an adopted child and the child's biological parents.
• noun An instance of such an adoption.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun An adoption in which the biological mother/biological parents and the adoptive family know each other's identities, and choose to remain in contact after the adoption process is finalized.