Turbulent mixed convection in channel flows with heterogeneous surfaces is studied using direct numerical simulations. The relative importance of buoyancy and shear effects, characterised by the bulk Richardson number Rib, is varied in order to cover the flow regimes of forced, mixed and natural convection, which are associated with different large-scale flow organisations. The heterogeneous surface consists of streamwise-aligned ridges, which are known to induce secondary motion in the case of forced convection. The large-scale streamwise rolls emerging under smooth-wall mixed convection conditions are significantly affected by the heterogeneous surfaces and their appearance is considerably reduced for dense ridge spacings. It is found that the formation of these rolls requires larger buoyancy forces than over smooth walls due to the additional drag induced by the ridges. Therefore, the transition from forced convection structures to rolls is delayed towards larger Rib for spanwise heterogeneous surfaces. The influence of the heterogeneous surface on the flow organisation of mixed convection is particularly pronounced in the roll-to-cell transition range, where ridges favour the transition to convective cells at significantly lower Rib. In addition, the convective cells are observed to align perpendicular to the ridges with decreasing ridge spacing. We attribute this reorganisation to the fact that flow parallel to the ridges experience less drag than flow across the ridges, which is energetically more beneficial. Furthermore, we find that streamwise rolls exhibit a very slow dynamics for Rib = 1 and Rib = 3.2 when the ridge spacing is of the order of the rolls' width. For these cases the up- and downdrafts of the rolls move slowly across the entire channel instead of being fixed in space, as observed for the smooth-wall cases.