Salivary gland tumors are diagnostically challenging due to major diversity of benign and malignant tumors with enormous intra-tumorous and inter-tumorous heterogeneity and, hence, frequently overlapping histologic features. DNA methylation has greatly enhanced tumor classification in several organs and led to the identification of previously unrecognized entities. In a recent study on DNA methylation of salivary gland tumors, we had identified a group of unclassifiable tumors. In this study, we characterize this group through an integrated analysis of clinical, histomorphologic, immunohistochemical, and molecular features. This group of 12 tumors is characterized by small, clinically benign appearing tumors with striking female predominance (91.7%), the latter not paralleled in other salivary tumor types. In addition to distinct DNA methylation profiling, copy number analysis revealed unique alterations with highly recurrent chromosome 5p/5q loss and frequent amplification of the MDM2 locus on chromosome 12q. Whole-exome and transcriptome sequencing detected no recurrent mutations or fusions. The histomorphologic features were only moderately distinct, comprising an obligate, thereby variable admixture of biphasic-tubular and monophasic-myoepithelial areas, low or absent nuclear atypia, and minimal proliferation. Frequent invasive behavior, a solitary lymph node metastasis, and the molecular alterations, altogether, strongly support classification as a, presumably low-grade, carcinoma. Altogether, these findings clearly distinguish this tumor group from histomorphologically similar tumor entities, in particular myoepithelial carcinoma, epithelial-myoepithelial carcinoma, and adenoid cystic carcinoma. We present thorough arguments that this tumor group represents a distinct salivary carcinoma entity rather than a variant of an existing one. We propose the provisional designation "Biphasic myoepithelial carcinoma with 5p/5q loss" for discussion.