The quote from your page seems to indicate 1.5 but it’s probably for the plywood.
“we can offer to produce any commercially available natural or reconstructed veneer… pressed on to plywood, particleboard or MDF in thicknesses from 1.5mm – 33mm (customized thickness can be made too).”
3mm is the thinnest mdf I’ve seen. If you want 1.5 you may have to use signboard, converd board is available in 1.5mm in 2400×1200 sheets. It cuts nicely with knife type cnc, not sure how you’ll go with rotary cnc cutters. Other card type boards like canson which is used as backing boards for picture framing might work too.