What is the reason for wanting to grow them together? if the anaerobes are obligate then its best to use an enrichment medium/liquid broth they will grow at the bottom and microphiles will grow from surface,then subculture onto selective media. l could help further if you state the bacteria name,yeasts are not normally a problem.
We are using strains isolated from human gut, we cant use selective media as we will be growing mixed culture. We would like to study mutual interaction and synbiotic effect of these strains together using different substrates.
It all comes down to finding an O2 concentration where both are at least a bit happy. In my experience the best way to try is in an anaerobic cabinet (like the ones Don Whitley Scientific supplies). You can use those completely anaerobic, but with a bit of imagination you can play with the atmosphere composition in a controlled way. (You have to remove the O2 absorbent for the chamber).