Is there a way to make the interior of selected polygons partially transparent as there is with polygons of a layer?
This could quickly be accomplished by having two layers in your MXD, one with the selection (with transparency applied) and one without your selection. In the layer properties>display tab, there is a transparency setting you can manipulate to give you a transparency effect on your selected features.
In the example I proposed, you would have two layers in the TOC that point to the same feature class with different transparency settings.
Layer 1 Copy - Contains only features you wish to display w/transparency. Set transparency level (e.g. 40%).
Layer 1 - Contains all features except those you wish to make transparent.
You'd want to use a definition query in each layer to query out the desired features. This is kind of a workaround solution, though it is one that I myself have used to achieve this result.
More info here.