1.5" MDF will typically be available via special order. Even at cabinet shops where 1" MDF can be found, anything thicker is special order unless you go direct to a distributor. Glueing together multiple .75" pieces are fine. I don't think you'll want to single-handedly handle/lift a 1.5" MDF 4x8' sheet, it'll be about 150lbs!!
As for glue, people have used anything from white elmer's craft glue, titebond I and II, G2 flexible epoxy and even Alex Plus caulk sealant. Either way there will be sooo much glue surface area that almost anything will create a strong bond.