Alemtuzumab Plus Fludarabine and Melphalan With or Without Cyclosporine, Mycophenolate Mofetil, and Low-Dose Total-Body Irradiation Therapy Followed by Donor Peripheral Stem Cell Transplant in Treating Patients With Hematologic Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed hematological malignancy of 1 of the following types: * Acute myeloid leukemia meeting at least 1 of the following criteria: * Poor-risk cytogenetics, including -5, 5q-, -7, 7q-, 11q23, and Philadelphia (Ph) chromosome-positive in first or subsequent complete remission (CR) * Relapsed or primary refractory disease with ≤ 10% blasts in the peripheral blood and ≤ 20% blasts in the bone marrow * Standard-risk cytogenetics in second CR AND autologous transplantation is not feasible * Standard-risk cytogenetics in third or subsequent CR * Acute lymphoblastic leukemia meeting 1 of the following criteria: * Second or subsequent CR * High-risk cytogenetics, including Ph chromosome-positive and t(4:11) in first CR * Relapsed or primarily refractory disease with ≤ 10% blasts in the peripheral blood and ≤ 20% blasts in the bone marrow * High-risk myelodysplasia * International Prognostic Scoring System Score ≥ 2.5 * Chronic myeloid leukemia (CML)\* with an inadequate response to imatinib meeting 1 of the following criteria: * Second or subsequent chronic phase * Accelerated phase NOTE: \*Patients with CML in blast crisis (\> 30% promyelocytes and myeloblasts in the bone marrow) are not eligible * Non-Hodgkin's lymphoma meeting 1 of the following criteria: * Primarily refractory disease or in refractory relapse * Relapsed disease after autologous stem cell transplantation * Chemosensitive relapsed disease without CR to standard salvage therapy AND no option for autologous stem cell transplantation due to blood or marrow involvement or failure to harvest sufficient autologous stem cells * Chronic lymphocytic leukemia meeting both of the following criteria: * Stage III or IV disease * Refractory to fludarabine * Multiple myeloma meeting 1 of the following criteria: * Primarily refractory disease or in refractory relapse * Relapsed disease after autologous stem cell transplantation * No relapsed disease \< 6 months after autologous stem cell transplantation * No available eligible HLA-matched (i.e., 5 of 6 or 6 of 6 antigen match for HLA-A, -B, and -DR loci) family donor by serological or molecular typing * Available suitable family donor meeting the following criteria: * Parent, sibling, or child of the recipient * ≥ 16 years of age * Identical for only one HLA haplotype (i.e., haploidentical) AND incompatible at the HLA-A, -B, -C, and -DR loci of the unshared haplotype by serological or molecular typing * Mismatched with respect to KIR class I epitopes graft-vs-host directional activity * Mismatching that predicts both graft-vs-host and host-vs-graft bi-directional activity eligible * No mismatching that predicts only host-vs-graft directional activity PATIENT CHARACTERISTICS: Age * 18 to 60 Performance status * ECOG 0-1 Hepatic * Bilirubin \< 2 times upper limit of normal (ULN) * AST and ALT \< 2 times ULN Renal * Creatinine ≤ 2 mg/dL Cardiovascular * LVEF \> 40% (corrected) Pulmonary * DLCO \> 50% of predicted Other * No active infection requiring oral or IV antibiotics * HIV negative * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception PRIOR CONCURRENT THERAPY: Biologic therapy * See Disease Characteristics Chemotherapy * See Disease Characteristics Endocrine therapy * Concurrent corticosteroids allowed for adrenal failure, treatment of graft-vs-host disease, or as premedication during study * No concurrent corticosteroids for antiemesis