Using transmission electron microscopy, we present an in-depth microstructural analysis of a series of Ga(Sb,Bi) epilayers and Ga(Sb,Bi)/GaSb quantum wells grown on GaSb(001) substrates by molecular beam epitaxy. Despite the dilute bismide compound Ga(Sb,Bi) is regarded as a highlymismatched alloy, we find that the material is of remarkable structural perfection, even up to 11%-14% Bi, the maximum Bi concentration incorporated into GaSb so far. No extended defects, nanoclusters, or composition modulations are detectable in the pseudomorphic layers. In addition, the quantum wells exhibit regular and homogeneous morphologies including smooth and stable interfaces with a chemical width on the same order as in other high-quality III-V heterointerfaces. These results may give reasons for the recent successful realization of mid-infrared lasers with room temperature operation based on the very same quantum well structures.