A method and apparatus for forming a profile that contains at least one layer of continuous fibers and at least one layer of discontinuous fibers are provided. Various features of the method are selectively controlled to achieve a profile that has increased transverse strength and flexural modulus. For example, the layer of continuous fibers is formed from one or more continuous fiber reinforced ribbons ("CFRT") that contain fibers embedded within a thermoplastic polymer matrix. The fibers are embedded within the matrix by a process that minimizes void fraction and in turn, optimizes flexural modulus. Further, the ribbon(s) are consolidated so that the continuous fibers remain fixed in alignment in a substantially longitudinal direction (e.g., the direction of pultrusion). In addition to enhancing the tensile properties of the profile, the use of such ribbons also allows the continuous fiber material to be more readily manipulated and placed into the desired position within the pultrusion die. The discontinuous fibers are also embedded within a thermoplastic matrix. Among other things, this may assist in bonding of the layers so that an adhesive is not required to achieve the desired strength. Also, rather being oriented in the longitudinal direction, at least a portion of the fibers are oriented in the transverse direction to provide increased transverse strength.