I'm trying to find a way to show relative line numbers as well as absolute line numbers, but not the way hybrid line numbers does it.
I want to see both at all times, probably each displayed on a column. Is this possible?
There is no way to have both absolute and relative numbers being displayed by Vim.
What you can do however, is to (ab)use the sign feature and display the relative numbers there. Note, since the sign column is limited to 2 characters, it won't work on very long windows with more than 100 lines.
There are a couple of plugins that enable it. The already mentioned RltvNmbr.vim from Dr. Chip, which was used to enable relative line numbering before that feature was available in Vim natively (around Vim 7.3 I believe). An alternative is to use my plugin DynamicSigns. This allows to flexible define what kind of signs will be drawn and when. Have a look at the example from this answer
Also, the sign column needs to be updated very often, which might impose a performance penalty. My DynamicSigns plugin tries to update the sign column as often as needed, but it might still be noticeable, if you scroll a lot. There is not much that can be done against it.