Combined strain and magnetization measurements on the Heusler shape-memory alloys Ni45Co5Mn38Sb12 and Ni44Co6Mn38Sb12 give evidence for strong magneto-structural coupling. The sample length changes up to 1% at the martensitic transformation, between a ferromagnetic, austenitic phase at high temperatures and a weakly magnetic, low-symmetry martensitic phase at lower temperatures. Under moderate uniaxial stress, the change in the sample length increases to and saturates at about 3%, pointing to stabilization of a single martensitic variant. A reverse martensitic transformation can also be induced by applying magnetic field: we find that within the temperature range of thermal hysteresis of the martensitic transformation, applying a field can induce a metastable expansion of the sample, while at slightly lower temperatures, the field response is reversible. These findings provide key information for future use of Ni(Co)-Mn-Sb-based Heusler compounds in, e.g., actuators and mechanical switches.