Reconciling one-dimensional valence with distinct mechanisms for reward/punishment
A meta-analysis of 397 neuroimaging studies was just published looking at this very question (see here).

They tested three hypotheses: 


Bipolarity - negative and positive are on the same continuum
Bivalence - negative and positive are independent
Affective workspace - valence is supported by a "flexible set of valence-general regions".


Their analyses are rather complicated, but they didn't find much support for the bipolarity or bivalence hypotheses.  Instead, in support of the affective workspace hypothesis, they conclude (emphasis mine):


  These findings suggest that, at the level of regional brain activity, there is no single region or even voxel that uniquely represents positivity or negativity. Limbic tissue, including the anterior insula, rostral ACC/ventromedial prefrontal cortex, dorsal ACC, amygdala, ventral striatum, as well as several other regions including the thalamus and occipitotemporal cortex, appears to contain cells that are part of the brain’s valence-general affective workspace or “affective neural reference space


But they note that some brain regions have preferences for negativity or positivity, meaning that these brain regions may tend to represent negativity or positivity over the other.

This meta-analysis isn't definitive, but it's the best we have right now.