You may know that asbestos-cement shingles can cost a bundle to remove and properly dispose of.
Consequently, the most common and least expensive solution is to leave the original asbestos shingles in place and remove only the aluminum siding; this way you'll avoid the hazardous dust created by tearing the shingles off. Instead, cover the shingles with polystyrene-foam insulation panels, then hang the new vinyl siding using 2-in.-long nails.
For more information go to Environmental Health & safety in the Home at www.ehso.com/ehshome/contents.htm and look at the asbestos pages (under "A")