This phase II trial studies how well sirolimus, cyclosporine and mycophenolate mofetil works in preventing graft-vs-host disease (GVHD) in patients with hematologic malignancies undergoing donor peripheral blood stem cell (PBSC) transplant. Giving chemotherapy and total-body irradiation before a donor peripheral blood stem cell transplant helps stop the growth of cancer cells. It may also stop the patient's immune system from rejecting the donor's stem cells. When the healthy stem cells from a donor are infused into the patient they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells. Giving total-body irradiation together with sirolimus, cyclosporine, and mycophenolate mofetil before and after transplant may stop this from happening.