<<Does this mean that you may dispatch to a field that is estimated to be below landing minimums so long as your alternate is forecast to be above minimums?>>
Yes, altho in this case two alternates are generally required.
This would be indicated in the respective air carriers individual operations specifications.
In addition, in the above listed case, and also depending on the specific wording of the ops specs, enroute re-dispatch might not be allowed.
The FAA gives their aircarrier inspectors rather broad latitude with respect to an individual airline's operations specifications.