Patients undergo evaluations to determine the extent of their disease and the status of their immune system. Patients then receive IFN-B subcutaneously once a day at one of three different dose levels. Patients also take AZT at 1 of 2 doses. The first 12 patients are treated with the lower dose of AZT. The first 4 patients are entered at level 1 of IFN-B. If no dose-limiting toxicity is seen in these 4 patients after 2 weeks of therapy, 4 patients are then enrolled at level 2 of IFN-B. The study proceeds in this manner until the highest tolerated dose or level 3 is reached. If both drugs are tolerated, patients then remain on both medications as long as they continue to tolerate the medications and show some improvement in either antiviral response, immune response, or clinical response for as long as 24 weeks. The initial three doses of IFN-B are given to each patient at the study site during which time the patient is trained to self-administer the IFN-B. Patients are then seen weekly for 4 months and every 2 weeks thereafter.