Square shaped layout border with round inside edges

I’m attempting to create a layout border with corners that are square on the outside and round on the inside. I’ve gathered that I need to create an .xml drawable definition composed of two shapes: one with a stroke width and corner radius and another with a stroke width only:

The drawables

round_border.xml

<shape xmlns:android="http://schemas.android.com/apk/res/android">
    <stroke android:width="4dp" android:color="#FF000000" />
    <padding android:left="7dp" android:top="7dp"
            android:right="7dp" android:bottom="7dp" />
    <corners android:radius="4dp" />
    <solid android:color="#FFC0C0C0" />
</shape> 

square_border.xml

<shape xmlns:android="http://schemas.android.com/apk/res/android">
    <stroke android:width="2dp" android:color="#FF000000" />
    <solid android:color="#FFC0C0C0" />
</shape> 

Each of these works independantly as a border when appliedby itself like so:

android:background="@drawable/round_border" 

but when they either or both are added to an item-list drawable like so:

composite_border.xml

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://schemas.android.com/apk/res/android">
    <layer-list>
        <item android:drawable="@drawable/round_border"/>
        <!-- <item android:drawable="@drawable/square_border"/> -->
    </layer-list>
</shape> 

and:

android:background="@drawable/composite_border"

The layout's background is completely black instead of just a black border.

Does anyone know how to make the layer list work for this task?