We use integrated digital image correlation (IDIC) with gradient-free optimization to identify the in-plane, linear-elastic material parameters of carbon fiber-reinforced polymer (CFRP) plates. With IDIC, a monolithic least-squares problem is formulated, based on the video capture of a tension/compression test, with the material parameters as unknowns. Transverse deformations are induced by using holeplate specimens, so that all parameters are identified with one tensile test. We also demonstrate how an invariant-based CFRP model, parameterized by the Tsai modulus, further enhances the robustness of IDIC characterization.