All modern internet connections make use of what is called a full-duplex communication system. This means, for example, that computer A can send information to another computer B at the same time that computer B is sending information to computer A. This is enabled by the physical implementation of all modern networks, which separates the signaling for sending and receiving data.
Aspera transfers are accordingly full-duplex. Because of this, you can make uploads and downloads at the same time without splitting your bandwidth capacity.
For example, if you have a 100Mbps link, you will have 100Mb available for incoming transfers and 100Mb available for outgoing transfers, even if they occur simultaneously.