The representation of stratocumulus clouds, and of the stratocumulus to cumulus transitions which are ubiquitous features of marine boundary layer clouds, remains a challenge for climate models. We show how a mass flux representation of boundary layer convective structures combined with an eddy diffusivity scheme, the "thermal plume model," first developed to represent cumulus clouds, can also adequately simulate stratocumulus and the stratocumulus to cumulus transition in a climate model. To achieve this, the detrainment formulation, in which detrainment increases for increasing negative buoyancy, has to be slightly modified: the buoyancy of a thermal plume parcel of air is computed by comparing the virtual potential temperature v,th of the parcel with that of the surrounding environment v,env at a given distance above instead of at the same level. This is consistent with the picture of detrained air parcels that experience some overshoot and reach a final destination at a level lower than the one at which they effectively leave the cloud or organized convective plume. The impacts of this modification are documented both for selected cases of stratocumulus, in comparison with large-eddy simulations, and in full 3-D climate simulations, in comparison with satellite observations of cloud cover. The modified scheme provides a uniform treatment of the dry convective boundary layer, of cumulus clouds, of stratocumulus, and of the transition from stratocumulus to cumulus. It is included in the most recent version of the LMDZ atmospheric general circulation model.