DISEASE CHARACTERISTICS: - Acute lymphocytic leukemia (ALL) with documented chemosensitivity (complete response [CR], partial response [PR], or minor response [MR]) in first or second remission, first or second relapse, or high risk ALL with Ph positive 9/22 translocation; OR - Acute myelogenous leukemia (AML) with documented chemosensitivity (CR, PR, or MR) in first or second remission, or first or second relapse; OR - Chronic myelogenous leukemia (CML), chronic or accelerated, that is not in blast crisis; OR - Hodgkin's disease or non-Hodgkin's lymphoma with documented chemosensitivity in first or second relapse Consenting human lymphocyte antigen (HLA)-identical related donor required No active central nervous system (CNS) or skin leukemia involvement No disease that requires additional mediastinal radiation