Polymerizable compositions are provided that contain an epoxy compound and a polymerizable, ethylenically-unsaturated resin having an acid functional group where the epoxy compound is polymerized by cationic polymerization initiated by the acid functional group and the polymerizable, ethylenically-unsaturated resin is polymerized by free-radical polymerization. To that end, a two-part polymerizable composition is provided that has a first part containing the epoxy compound; and a second part containing the polymerizable, ethylenically-unsaturated resin having an acid functional group. The first part and/or the second part further contain a radical initiator effective to initiate either self-curing or light-curing by free-radical polymerization.