Old asphalt floor up, what can i put down before tiling?

Hi, iv started to chip an old cracked asphalt floor up in my hallway, i will be left with an uneven concrete base. My plan is to put timber batons down in a grid form, all level with an existing floor so i can pour a concrete mixture in and screed off and tile over, but im worried because as im taking the asphalt up it looks like some form of dpm is coming up with it. Now i dont want to put a sub floor on top of the old concrete base if it is the dpm that im taking up. Basically im after some info on a decent dpm to put down if needed and what kind of subfloor can i put on top that can only be about 30mm-50mm (ish) deep?

Thank you