In the first hemistich the subject of comparison is the cheek, and the model is Syrian paper. In the second the subject is the animal’s lip, and the model is prepared Yemeni leather. The comparative prefix kāf marks both relationships.
A crude statement that the face “is paper and leather” misses the literary technique. The intended shared attributes differ: the cheek is likened to paper for its smoothness, and the lip to leather for its finely finished edge.