does minHeight do anything?

I don’t know all your exact requirements, but it seems you can solve this with another layer pretty much like in your diagram. Set the minHeight on an outer layout and then just fill_parent/match_parent on the inside. Maybe something like:

<LinearLayout
    android:orientation="horizontal"
    android:layout_height="wrap_content"
    android:layout_width="wrap_content"
    android:minHeight="150dp">
    <LinearLayout
        android:orientation="vertical"
        android:layout_height="fill_parent"
        android:layout_width="wrap_content">
    </LinearLayout>
    <ImageView />
</LinearLayout>