The parents, who can't be named for legal reasons, allege the two boys were taken from them because of their faith, views on discipline and because they took them to church.
The charity Christian Concern is supporting the couple at a Court of Appeal hearing to seek permission for their case to be heard before appeal judges.
Christian Concern said the couple had raised their own family before deciding to adopt and had cared for the brothers for over three years before they were taken into care in summer 2014.
The case was already heard in a Family Court but a judge refused to return the children to their adoptive parents because a psychologist's report recommended against it.
The couple will ask the Court of Appeal for a second psychologist's report.
They will allege that they were not kept properly informed about the investigation conducted by social services, and were not given a proper opportunity to explain their parenting methods.
"Many of the accusations levelled against us by social services during the investigation have been simply not true or have been blown out of all proportion," they said.
"To make it worse, on the basis of one psychologist's report, the judge has ruled that our parenting isn't appropriate.
"Our boys have already been through tremendous stress in their lives and since their removal from us, they have been in a state of 'high anxiety'.
"We dearly love our boys and we want the best for them. We will do what it takes to ensure that justice is done."
Andrea Williams, chief executive of Christian Concern, said: "We are seeing a worrying trend whereby Christian parents are being treated with suspicion because of their faith.
"These Christian parents who had adopted two boys were treated as if they were not the 'real' parents.
"Their views on disciplining the children and taking them to church were wholly disrespected by the social services and now tragically their children have been taken away.
"It is time for a change regarding the secrecy surrounding child courts. Their secretive nature means that injustices can be covered up, and it is time for this to be reviewed."
The full details of the case cannot be revealed in order to protect the identity of the two boys.