Recycling plastic trash bags?

We used to have access to the recycling bins, so I would just put my recyclables in a paper grocery bag and take them to the bin myself. But now my apartment is forcing us to put our recycling in plastic trash/recycling bags for our valet trash to pick up. This doesn't make sense to me. Will the city of Houston recycle the plastic bags? Or will it end up in the landfill with the rest of the garbage?