In the long run it may be better to lift that subfloor and replace it. The black adhesive, depending on how old it is may contain some asbestos.

In order to have a successful tile installation you will need a MINIMUM of 3/4" underlayment rated plywood (hint - CDX isn't) over floor joists that are 16" on center. The size of the joist will depend on its unsupported span but it should be at least a 2x8, much better if a 2x10. On top of the plywood you could set the 1/4" cement board like Hardibacker following their installation instructions by using thinset under the board and taping the seams with a fiberglass mesh tape.

Many thanks for the advice!