Impossible to tell what is the subfloor. But from the picture, you basically have a vinyl roll goods floor installed with black emulsion ashesive over the wood subfloor. The pattern is actually a very thin layer of vinyl, the white in the picture is the backing to the flooring, and the black is the adhesive.
The white backing is not going to come up very easily. It will tear into pieces, no matter what you do. There are floor tile chippers you can rent, but what I would have done is leave the floor intact, and install a new 1/4" subfloor right over the top. That is assuming the existing floor is in good condition and solidly adhered to the floor. Nail it down every 4" on the perimeter of the sheet, and every 8" throughout the field of the sheet, use a subfloor crack filler between sheets and over the nail holes, and presto, you're ready for the new flooring, whether it be roll goods, vinyl tile, or laminate. If you want to do ceramic, use 3/4" plywood rather than 1/4", and you'll need to use a mrble saddle or similar at the doorway.