Grammar – ‘By Their Side’ vs ‘By Their Sides’: Proper Usage

'Two sides of the same coin' does not quite mean what you describe.

two sides of the same coin - different but closely related features of one idea

It essentially means that two things are the same. I might use it in a context where someone is describing someone else as both 'lazy' and 'messy' and in response I could say that those are 'two sides of the same coin' and thereby suggesting that they are one and the same, in this case suggesting that the person is messy because they are lazy.

As far as I can tell you want a pithy phrase to describe two things that are good together but not necessarily either good or as good apart.

I'd suggest a simile in this situation. A very common type of phrase is to say:

[Something] without [something] is like [something else] without [something else].

Currently on the London Underground for example there is an advert that says something along the lines of 'a woman's hair without product x is like rock without roll' (the latter part usually a ridiculous separation for humour value). There's no standard phrase used here but it's an opportunity to be creative.

A couple more examples:

A man without ambition is like a bird without wings (from a 1908 business magazine)
A house without books is like a room without windows (a proverb that goes back even further)

surface is the least appropriate term to use: it really refers to the upper or outside layer of something. You could talk about the entire surface of the cuboid (all six faces) as one surface.

For side, even the major dictionaries disagree about what it means:

flat outer surface of an object, especially one that is not the top, the bottom, the front, or the back Cambridge Dictionary

An upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. Oxford dictionary

So, a cuboid could have either two sides (left and right) or four sides (left, right, front and back).

In everyday speech, face is used to describe the front of an object, however in geometry it is used in the way that you require- for example:

A polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices. Wikipedia

All of these terms are therefore prone to some confusion, but if you wish to describe each of the six faces using the same term, face is probably the best term to use.