I'd like to cite a technical blog post that was published in three parts, however, the parts don't have links to each other. Should I cite them separately as if they were different articles, or is there a way I could somehow combine them? E.g., if I were to use the main title of the series, and include a list of all 3 URLs.
It's a computer science undergraduate honours thesis, if that's relevant.
You have two options that are IMHO equally good. Either cite them as one item with three links:
[1] J. Doe: Foo bar (I., II., and III.), 2015, http://example.net/blog/1 , http://example.net/blog/2 , http://example.net/blog/3 [2015-04-17].
Or cite them as three items:
[1] J. Doe: Foo bar, part I., 2015, http://example.net/blog/1 [2015-04-17].
[2] J. Doe: Foo bar, part II., 2015, http://example.net/blog/2 [2015-04-17].
[3] J. Doe: Foo bar, part III., 2015, http://example.net/blog/3 [2015-04-17].
If they were three articles in an article series, they would be cited as three items for sure. But for blog posts, no canonical citation style is established (or maybe some style mention it, but it's not a universally accepted thing); this means that any style that contains the relevant information is OK.
As for me personally, I would probably stick to the second variant, unless you commonly cite multiple items with one number (some chemists and engineers do this).
