Partially HLA-Matched Irradiated Allogeneic Cellular Therapy After Reduced Intensity Total Body Irradiation

DISEASE CHARACTERISTICS: * Patients over 18 years old must meet the following criteria: * Histologically confirmed hematologic malignancy and not a candidate for a standard allogeneic transplantation * High-risk disease, including: * Refractory/relapsed acute myeloid leukemia (AML) or AML in second or greater completion remission (CR2) * Relapsed or refractory acute lymphoblastic leukemia (ALL) or ALL in CR2 * Tyrosine kinase inhibitor-resistant chronic myelogenous leukemia in chronic, accelerated, or blast crisis * Fludarabine-resistant chronic lymphocytic leukemia * High-risk myelodysplastic syndrome (MDS) (i.e., MDS with a score ≥ 1.5 by the International Scoring System) * Chronic myelomonocytic leukemia * Relapsed diffuse large cell non-Hodgkin lymphoma (NHL) with measurable disease after (or not eligible for) high-dose chemotherapy/autologous hematopoietic stem cell (HSC) rescue or allogeneic hematopoietic stem cell transplantation (HSCT) * Relapsed follicular NHL, mantle cell lymphoma, or low-grade histology NHL with measurable disease after (or not eligible for) high-dose chemotherapy/autologous HSC rescue or allogeneic HSCT * Relapsed or refractory high-grade/aggressive NHL (Burkitt lymphoma, lymphoblastic lymphoma, T-cell lymphoma, NK-like lymphoma) with measurable disease after (or not eligible for) high-dose chemotherapy/autologous HSC rescue or allogeneic HSCT * Hodgkin lymphoma with measurable disease after (or not eligible for) high-dose chemotherapy/autologous HSC rescue or allogeneic HSCT * Relapsed or refractory multiple myeloma after (or not eligible for) high-dose chemotherapy/autologous HSC rescue and following salvage therapy with thalidomide, lenalidomide, bortezomib or other FDA-approved multiple myeloma salvage therapies * Patients 13-17 years old must meet the following criteria: * Histologically confirmed hematologic malignancy and not a candidate for a standard allogeneic transplantation * High-risk disease, including: * Refractory/relapsed AML or AML in CR2 * Relapsed or refractory ALL or ALL in CR2 * Relapsed diffuse large cell NHL with measurable disease after (or not eligible for) high-dose chemotherapy/autologous HSC rescue or allogeneic HSCT * Relapsed follicular NHL, mantle cell lymphoma (or low-grade histology NHL) with measurable disease after (or not eligible for) high-dose chemotherapy/autologous HSC rescue or allogeneic HSCT * Relapsed or refractory high-grade/aggressive NHL (Burkitt lymphoma, lymphoblastic lymphoma, T-cell lymphoma, NK-like lymphoma) with measurable disease after (or not eligible for) high-dose chemotherapy/autologous HSC rescue or allogeneic HSCT * Hodgkin lymphoma with measurable disease after (or not eligible for) high-dose chemotherapy/autologous HSC rescue or allogeneic HSCT * Eligible for haploidentical irradiated cellular therapy * No known active brain metastases or malignant meningitis * Available partially (≥ 3/6 class I antigen) HLA-matched (by serology) related donor NOTE: A new classification scheme for adult non-Hodgkin's lymphoma has been adopted by PDQ. The terminology of "indolent" or "aggressive" lymphoma will replace the former terminology of "low", "intermediate", or "high" grade lymphoma. However, this protocol uses the former terminology. PATIENT CHARACTERISTICS: * ECOG performance status (PS) 0-2 * Karnofsky PS 60-100% (for patients \> 16 years) or Lansky PS 60-100% (for patients ≤ 16 years) * Patients who are unable to walk because of paralysis but who are up in a wheelchair will be considered ambulatory for the purpose of assessing PS * Patients ≥ 18 years: * Total bilirubin \< 1.5 times upper limit of normal (ULN) (unless attributable to Gilbert disease) * DLCO/alveolar volume \> 50% * Serum creatinine \< 2.0 mg/dL * Patients 13-17 years: * Creatinine clearance or radioisotope GFR ≥ 70 mL/min OR serum creatinine based on age/gender as follows: * 13 to \< 16 years: 1.5 mg/dL (male) or 1.4 mg/dL (female) * ≥ 16 years: 1.7 mg/dL (male) or 1.4 mg/dL (female) * AST/ALT ≤ 2.5 times ULN for age * Total bilirubin \< 2.0 mg/dL (unless attributable to Gilbert syndrome) * Shortening fraction ≥ 27% by ECHO or ejection fraction ≥ 50% by radionuclide angiogram * FEV\_1, forced vital capacity, and DLCO corrected for hemoglobin ≥ 60% by pulmonary function tests (PFTs) * Children unable to cooperate for PFTs must meet the following criteria: * No evidence of dyspnea at rest * No exercise intolerance * No requirement for supplemental oxygen therapy * Any other organ dysfunction thought to be secondary to disease will be considered separately and the patient will be eligible at the physician's discretion * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception before, during, and for 24 weeks after study treatment * No known HIV positivity * No history of current or prior medical problems that, in the investigator's opinion, would prevent administration of study treatment or assessment of response due to excess toxicity * No active uncontrolled infections or other medical, psychological, or social conditions that might increase the likelihood of patient adverse effects or poor outcomes PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No corticosteroids within 2 weeks before receiving irradiated donor lymphocyte infusion * No medications that might increase the likelihood of patient adverse effects or poor outcomes