I had brichardi breed in a 65 gallon tank with kenyi and socolofi. I later moved them into a 35 gallon of their own and their colony flourished, but they weren't exactly languishing before that. It might not be recommended to mix them, but brichardi are tough and mbuna are usually most interested in messing with their own kind. You might need to keep diet in mind, though. Most mbuna would want more vegetable matter in their diet, while brichardi would want more of a carnivore blend. Of course, you could get around this by offering plants, algae, sinking spirulina, and spinach leaf to the mbuna as a complement to a more fish-heavy general flake. The occasional mysis shrimp feast would benefit everyone, too.
The problem in mixing them is when the fry are free swimming. They brichardi will attempt to take as large a territory as possible, in some cases vanquishing fish to the corners or killing them. In the above example, kenyi and socolofi are pretty aggressive mbuna, so they can usually hold their own. Problem with aggressive mbuna, is they eventually find out that brichardi fry taste good... and then you'll have a real fight on your hands. A 5"+ male kenyi won't back down from regular brichardi, and can beat them in a straight fight, on his way to the buffet. The conditions are not ideal for either types.