There have been some questions and movement on some case but it's not currently possible for a non-marrids couple to adopt jointly. (it not illegal but it doesn't happen currently).
http://www.hrc.org/issues/parenting/adoptions/8464.htmPermits a same-sex couple to jointly petition to adopt? Possibly.
A Michigan appellate court has ruled that Michigan law only allows couples married to each other to petition jointly to adopt. (In re Adams, 473 N.W.2d 712 (Mich. Ct. App. 1991)).
However, another, more recent case, suggests there can be different outcomes. In Hansen v. McClellan, a biological mother terminated her parenting rights so that she and her partner could jointly petition to adopt her children. A court granted the adoption. After the dissolution of the couple’s relationship, the mother attacked the grant of adoption, arguing that the court lacked the power to grant an adoption to an unmarried couple. The Court of Appeals held that the circuit court had the subject matter jurisdiction to hear the initial adoption proceeding. Accordingly, the issue of whether it was correct to grant a joint adoption to an unmarried couple could only have been attacked on direct appeal, which the mother did not do. Therefore, the mother was unable to collaterally attack the grant of adoption. This does not necessarily mean that the statute allows joint adoptions by same-sex couples.However, it does show that at least one Michigan court has permitted this. (Hansen v. McClellan, No. 269618, 2006 WL 3524059 (Mich. Ct. App. December 07, 2006))
In 2004, the state Attorney General issued an opinion stating that same-sex couples who are married from other jurisdictions are not legally authorized to adopt children in Michigan as a couple, but that one member of a same-sex couple could adopt a child in Michigan as a single person.
2004 Mich. Op. Att'y Gen. 7160
Permits a same-sex partner to petition to adopt partner’s child or child of the relationship? No explicit prohibition.
No explicit prohibition, however one judge has acted to block such adoptions. On June 4, 2002, Archie Brown, the chief judge of Washtenaw County, ordered all county judges to stop granting second-parent adoptions to unmarried parents because the practice violated state law. Brown then transferred all pending second-parent adoption cases to himself to ensure that his directive be enforced. The Michigan American Civil Liberties Union (ACLU) filed a motion challenging his authority to transfer the cases. Brown promptly rejected the motion. It appears that no petitions for second-parent adoptions have been filed since this time.