Here's a somewhat complex, but single object effect....
I'll outline how to do it with only a rectangle first so it's a bit clearer. Then near the end I'll explain how to change things when working with a group of objects.
Start with your rectangle.
Open the Appearance Panel (
Window > Appearance) if it isn't already open. And click the "New Fill" button on the bottom of the panel.
You should see a second "Fill" item appear in the panel. Highlight the new fill and adjust the color (I changed it to white), make certain it's above the other items by click-dragging it to the top if needed.
With the new fill still highlighted, choose Effect > Convert to Shape > Ellipse... When you do this, you'll see the rectangle change to an Ellipse. Adjust the numbers in the effect to get the general size of ellipse you want. It will remain in the center of the rectangle for now. Don't worry about that yet. Just get the size relative close and click OK. Note any values in the screenshots here are specific to the rectangle I am using. Your'e values probably will not be the same.
With the new fill still highlighted choose Effect > Distort & Transform > Transform... The Transform Dialog will open. Tick "Preview" and then in the Move: Vertical filed enter a negative value so the ellipse moves off the top of the rectangle. Then click OK. Again, the values in my screenshots are specific to the objects I have. Your values will most likely be different.
Now, expand the new Fill item in the Appearance Panel (if it isn't already expanded) by clicking the little arrow next to it. And then click the "Opacity" link you see there. Reduce the opacity to a value you are happy with.
Now, at first glance you may think thats it, but it's not. Note what happens when I put another colored object behind the rectangle:
To fix this you need a couple more steps.
Select the rectangle and then choose Effect > Pathfinder > Crop. There will generally be a warning stating something about "this is normally applied to groups or type objects.. etc..." just ignore it and click ok. You should then see the crop item in the Appearance Panel. But the art hasn't changed.
The final piece of the puzzle is to click that Crop item in the Appearance Panel and drag it so it is below all other items in the panel. You want "Crop" to be below everything except the bottom "opacity" item.
Now, you'll undoubtedly notice the stroke has disappeared.
In order to get the stroke back you need to highlight the stroke item in the Appearance Panel, then using the Stroke Panel set the stroke to align to the inside. This will move the stroke inside the "crop" item so you can see it again. You may need to adjust the stroke weight to compensate for it now being on the inside.
This works on a single object. If you have multiple objects you must Group them first and then the steps are very similar.
Differences when working with groups.
Here is a group, containing live text and a rectangle, with the effect.
Note the placement of the Crop item and the extra fill (green). For a group, you need to highlight the top fill and choose Effect > Pathfinder > Add. Make certain the "Add" item appears under that top fill when it is expanded.
The highlight has changed a bit as well. Rather than being a solid fill, it is a gradient. A solid white fill won't work with a group. Note the Gradient Panel int he image above. the highlight fill is now a white to white gradient. One gradient stop is set to 0% opacity (in the Gradient Panel) the other gradient stop is set to 40% opacity (in the Gradient Panel).
This may seem very complex. However, once you do it a few times it gets easier.