I want to level & tile a fire hearth?

We've opened up the fire place in our play room and want to paint the brick inner and tile the floor/hearth. The floor was originally carpeted and then we've exposed the floorboards and they've been sanded and varnished. The hearth was basically dodgy concrete, which was in pieces, laid on top of a damp proof membrane. Below that is just sand. We've been told to fill the holes that go through to below ground level and then use a base of sand & cement wet mixed. We've done this and now I'm just wondering whether we should put back down, on top, the damp proof membrane? I've looked at other questions for preparing uneven floors for tiles and they all suggest using a floor leveling compound. It's suggested that should be good enough to use for tiling with either laying board first or buying a special cement prep for tiles? My problem is that my husband feels we should use the floor leveling compound straight on top of the sand & cement mix but I feel we should lay the DPM? He thinks it will shift as it's not adhered to anything as it will just sit on the dpm. Unfortunately I'm sure at some point in the past I'm certain this fire had a lovely stone hearth which we could have used as is or would have at least served as a solid base to start from! Any help on this would be really appreciated. Just a note that it's a small area not for general walking on but will be just a feature in the play room and the tiles will probably be white/grey brick tiles 15x7.5cm. Thanks