Subjects will be diagnosed with a hematological malignancy (cancer of the blood), which is unlikely to be cured with conventional non-transplant therapy. The best results of bone marrow transplant are obtained with the donor is a relative that has identical tissue type (HLA-type). These subjects will not have such a donor available but they will have a appropriately matching unrelated umbilical cord blood unit (UCB). However, the cord blood unit does not contain a high enough number of cells and may take longer to engraft (or grow). The purpose of this study is to determine whether the addition of stem cells from a family member to supplement a standard unrelated cord blood transplant is safe and will increase the success of the cord blood transplantation procedure. Subjects enrolled in this study will receive an unrelated cord blood transplant plus a haplo-identical (half-matched), T-cell depleted stem transplant from a related donor. The goal of this study is to determine whether the addition of the related stem cells accelerates bone marrow recovery and improves long-term disease free survival.