A method and apparatus for the additive manufacturing of three-dimensional objects are disclosed. Two or more materials are extruded simultaneously as a composite, with at least one material in liquid form and at least one material in a solid continuous strand completely encased within the liquid material. A means of curing the liquid material after extrusion hardens the composite. A part is constructed using a series of extruded composite paths. The strand material within the composite contains specific chemical, mechanical, or electrical characteristics that instill the object with enhanced capabilities not possible with only one material.