DISEASE CHARACTERISTICS: Hematologic malignancy, including acute myeloid or lymphoid leukemia of any FAB subtype, not in remission with chemotherapy or requiring bone marrow transplant OR Chronic myeloid leukemia, advanced beyond first chronic phase OR Myelodysplasia, including secondary to prior chemotherapy, with: Granulocyte count less than 500/mm3 OR Platelet count less than 50,000/mm3 OR High risk cytogenetic abnormalities such as +8, -7, -5, or 11q23 OR Intermediate or high grade lymphoma without response to initial therapy or in relapse OR Multiple myeloma without response to initial therapy or in relapse OR Stage IV low grade lymphoma or chronic lymphocytic leukemia not achieving remission with 2 regimens No aplastic anemia Related haploidentical donor (1-3 HLA-A, B, and/or DR mismatch) for collection of stem cells and whole blood T-cells required

PATIENT CHARACTERISTICS: Age: 6 months to 49 years Performance status: ECOG 0-2 Life expectancy: Greater than 12 weeks Hematopoietic: See Disease Characteristics Hepatic: Bilirubin less than 1.5 mg/dL SGPT less than 3 times upper limit of normal Renal: Creatinine less than 1.5 mg/dL Cardiovascular: Left ventricular ejection fraction at least 45% No symptoms or active treatment of left ventricular failure Pulmonary: Corrected DLCO at least 50% Other: No acute viral, bacterial, or fungal infection No prior transfusion associated graft versus host disease No other medical condition that would preclude study Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception

PRIOR CONCURRENT THERAPY: Biologic therapy: At least 3 weeks since prior immunotherapy or interferon alfa and recovered No prior autologous or allogeneic progenitor cell transplant Chemotherapy: See Disease Characteristics At least 3 weeks since prior chemotherapy and recovered Endocrine therapy: Not specified Radiotherapy: At least 3 weeks since prior radiotherapy and recovered Surgery: Not specified