Best way to cover basement tiles containing asbestos
adrex feather finish, is what i use to encapsulate asbestos tile and old cut back adhesive. just be sure skim it thick enough. It appear ppl don't like my ardex answer, well let me explain further. 
FLOOR LEVELER is not the best choice for your situation becuase, its likely that the asbestos tile are bonded to the older black adhesive. The tiles are easy to pop off that glue, that means its good odds the floor leveler will begin to break apart, now you have a crunchy floor. Using a highly modified skim coat give more flex ability and better adhesion. Floor leveler can work a lot of the time but you have to adjust to the job conditions. In this case its a gamble using a floor level if tiles aren't well bonded. You will spend alot of time and money to give your self a 50/50 shot it fails. Adex is less cost, time, and is absolutely rated for this very thing. Leveler needs a primer coat and its likely that tiles filthy and have some kind of finish added to it. The prep needed to insure a good bond can't be done because it will disturb the old floor. You being the home owner mean you can take out a certain amount, where i live its only 15sqft but may be different where you live. Its worth calling a abatement company to find out. Work the with what the job gives you, their all different.