It is a little more complicated than that, but not much.

You can not really compare it to mono and stereo as its really a different animal.

Unbalanced signals contain a single signal, and a grounding.

Balanced signals contain 2 signals - hot and cold, and a grounding. This still carries just a mono sound source, where the hot wire carries the original sound, and the cold wire carries the inversion of the exact same sound. I wont go into detail of this unless you want me to do, but basically it is a method which is used to remove noise from a single mono sound source.

So in order to carry an unbalanced signal you need a cable with at least 1 single core wire for the mono signal, and a shield for the ground.

In order to carry a balanced signal you need a cable with at least two cores, to carry the hot and cold signal, and a shield or grounding.

What you probably know as a mono jack, is actually called a TS jack, which stands for Tip-Sleeve which allows connections to two wires, which is generally the single core and the sleeve.

What you probably know as a stereo jack, is actually called a TRS jack, which stands for Tip-Ring-Sleeve which allows connections to three wires, which is generally two core wires and the shielding/ground.

A single stereo socket, like a headphone socket on your mixer takes a TRS jack because it uses the three wires to carry Left, Right, and Ground.

With the exception of headphone sockets, stereo signals are rarely output on TRS sockets in pro audio equipment. Usually every input and output will be mono, and either balanced or unbalanced depending on the equipment.

So if your sound card has two balanced outputs, you could use this for 2 mono signals, or 1 stereo signal. You need to use 2 connections for a stereo signal regardless generally.

If you connect a TRS balanced cable to an unbalanced output or input the cable will act just the same as a unbalanced TS cable.

Erm. Hope that makes sense. If not please ask. And it would make more sense if you explained exactly what you were trying to do. I might be able to explain it better detail.