I'm not sure what you're trying to describe. Do you have a graphic example?
You can adjust the blend mode and opacity of a bitmap in the Layers panel. You might try playing with blend modes to see if you can achieve the effect you're looking for.
Otherwise, it sounds like you're describing Path operations—like Add/Union, Subtract/Punch, Intersect, Crop—which are available in the Properties panel (or the Modify > Combine Paths menu). These can only be applied to paths, I believe, not bitmaps.
If you're looking to apply a path-type effect to bitmaps, you might be able to achieve it by combining two vector shapes (using one of the path operations above) and then applying the resulting compound shape as a mask to the bitmaps—placing the compound shape above the bitmaps, selecting all three objects and choosing Modify > Mask > Group As Mask.
Rereading your post, I think I may be understanding what you're trying to achieve: You have two overlapping bitmap images that you're compositing into a larger image—for example, creating one wide horizontal image out of two smaller horizontal images. At full opacity, the top image would cover up or cut off the image below it, creating a seamless though abrupt transition between the two images. But at less than full opacity, you can see the overlap.
If this is the case, then applying a mask to one of the images may be the answer. Use the rectangle tool to trace the image minus the portion you want removed, than select both the rectangle and bitmap and choose Modify > Mask > Group As Mask. The rectangle will now be masking the bitmap, hiding the portion you don't want shown. For best results, you may need to then select the mask thumbnail in the Layers panel and choose the "Path outline" option in the Properties panel.