stepfamily

A family where one or both parents have a genetically related child that is not genetically related to the other spouse. In some cases, both parents may have one or genetically related children that are not genetically related to the other spouse. The stepfamily designation parents may be discontinued to be used if the child or children have been adopted by the non-biological parent.
Children may have a relationship or in joint custody with both biological parents, meaning visitation rights or have a joint custody agreement where a child lives with one biological parent at a specific time, but they may only live with one biological parent at a specific time.

A stepfamily only occurs when there is a genetically unrelated parent. However, the use of the term may be discontinued if all the children of the family have been adopted legally by the non-biological parent.
A simple stepfamily is where only one of the spouses has a genetically related preexisting child or children and the other spouse does not. If the child or children have been adopted by the non-genetically related parent the stepfamily may be referred to as a family.
A complex or blended stepfamily occurs when both parents have biologically unrelated children at the start of the family. However, a simple stepfamily can become complex or blended when the two parents have a biologically related child in addition to the one or more child that is biologically unrelated to one of the parents.

I grew up in a stepfamily with one full sister and one halfsister, and one full brother and one halfbrother. I did not have a stepbrother until my father divorced my mother and married a woman with a son from a previous marriage.