If you select an image with the Direct Selection tool, you can lower the Opacity and change the Blending Mode of just that image without changing the Transparency of the Frame itself. So if the Frame has any Fill or a Stroke, they will still be 100% Opaque. But if you select a Frame with the Selection tool and apply Transparency, the Frame and everything contained in it will also be Transparent. Don’t believe me?
Select a Frame with a Fill and Stroke and lower its Opacity in the Transparency palette (Window > Transparency). Now, using your Direct Selection tool, select an image from another Frame that has no Transparency applied. Copy the image (Edit > Copy) and select your Transparent Frame with the Selection tool and paste the opaque image into it (Edit > Paste Into). The image takes on the Transparency of the Frame it has been pasted into.
Tip provided by Jeff Witchel, Certified Adobe® Training Provider.