There is only one set of audio inputs, though they can be used with both video inputs. A typical solution is to connect the audio outputs of both sources to the Slingbox, using Y connectors. Then, you have to ensure that only one of the sources is turned on at a time. If they are both on, you may hear a mixture of the two soundtracks, or badly distorted audio, depending on the devices. With a few devices, a Y connector won't work well, because one device will load down the other's audio output, even when turned off. In such cases, you'll need to use an external remote-controlled audio or A/V switching device.
I'm an audiophile from decades ago and long experience swapping leads with dire consequences has me nervous about Y-Splitters and other dubious work arounds!
At the moment my source is a Tivo which can not be turned off, so my 350 is reduced to one video/audio source and one silent video-only source on composite.
The online 350 Support section says:
"The Slingbox 350 is designed for only one A/V device at a time. However, you could use the remaining available video input (composite or component) for another device without sound, like a security camera, as long as it uses the proper connector."