We developed a machine learning algorithm (MLA) that can classify human thyroid cell clusters by exploiting both Papanicolaou staining and intrinsic refractive index (RI) as correlative imaging contrasts and evaluated the effects of this combination on diagnostic performance. Thyroid fine-needle aspiration biopsy (FNAB) specimens were analyzed using correlative optical diffraction tomography, which can simultaneously measure both, the color brightfield of Papanicolaou staining and three-dimensional RI distribution. The MLA was designed to classify benign and malignant cell clusters using color images, RI images, or both. We included 1535 thyroid cell clusters (benign: malignancy = 1128:407) from 124 patients. Accuracies of MLA classifiers using color images, RI images, and both were 98.0%, 98.0%, and 100%, respectively. As information for classification, the nucleus size was mainly used in the color image; however, detailed morphological information of the nucleus was also used in the RI image. We demonstrate that the present MLA and correlative FNAB imaging approach has the potential for diagnosing thyroid cancer, and complementary information from color and RI images can improve the performance of the MLA.