Third alternative to "between" and "among?"

This is a good place to use the lovely word gamut.

Houses in this neighbourhood run the gamut of colours from blue to orange to red.

As gamut means 'the whole scale or range' of a thing, you automatically include everything in between.

EDIT: To answer your edit, no, that just makes it sound like they vary between those three colours. You could say:

"Houses in this neighbourhood vary from blue to orange to red and everything in between."

"Spectrum"--it's particularly apropos for your color-based example, but can also work for any continuous scale:

Houses in this neighborhood cover the spectrum from blue to orange to red.

Another possibility would be to say "range from":

Houses in this neighborhood range from blue through orange all the way to red.