Both the vapour retarder and air barrier need to be maintained in the header areas. It is possible to do this with polyethylene sheathing, but it is very difficult to achieve and maintain a good air seal this way. A better method is to use rigid foam and expanding foam to seal each section of the header between the floor joists. Also seal any protrusions that come through the header. This also makes it much easier to seal around pipes and other penetrations.
Adding a layer of rigid foam on the interior to seal off the header increases the R-value of the headers and decreases heat loss through the headers.
When using rigid foam it is best to cut it either slightly smaller or on an angle in order to allow for a gap around the edge for the expanding foam.