See André, Chapter 14.
Mixed
AG (Algebraic geometry)
Check the abstract of Déglise and Cisinski, and their preprint
There might be two different notions of mixed Weil cohomology. See André and Déglise-Cisinski.
Add links to examples here.
Deglise and Cisinski said that they work on localization seq over general bases, and Cisinski said that they have basicly done it. He said in June 09 that he could send the statements if I wanted.
nLab page on Mixed Weil cohomology