I am creating a base interface for both the class
Download but I can't figure out what to call it. Is there an English word that can mean upload at the same time download?
I would recommend file transfer if you are transferring entire files, by analogy to FTP (File Transfer Protocol).
You want to distinguish what your interface does from general network communication, so data transfer is too generic.
Two possible terms: 1) bidirectional data transfer and 2) full duplex data transfer. Here's a good discussion in relation to USB 3.0.