I know its possible to spread 1 cell across multiple rows using the rowspan attribute, however is it possible to spread 2 cells evenly across multiple rows, without resorting to a nested table?
Sounds like this is what you are after:
If so, then no, technically speaking this isn't possible in HTML, however that's only because of how we are thinking of the rows.
Instead of 3 rows, if this table were actually 6 rows, then it would work if you adjusted the rowspans to:
Here's an example with a cell spreading across multiple rows and columns
This page is old but still explains how this works very well.
If that isn't what you're looking for then we'll need you to better explain why rowspan isn't what you're looking for.