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Wiktionary
open adoption

n. 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.

Wikipedia
Open adoption

Open adoption is a form of adoption in which the biological and adoptive families have access to varying degrees of each other's personal information and have an option of contact. In Open Adoption, the adoptive parents hold all the rights as the legal parents, yet the individuals of the biological and adoptive families may exercise the option to open the contact in varying forms: from just sending mail and/or photos, to face-to-face visits between birth and adoptive families.