Set the AlternationCount property of the ListView and use a trigger or bind to ItemsControl.AlternationIndex in order to set the background color.
Edit sorry miss read, I've changed the xaml below so the first item in the inner ListView is yellow.
<UserControl x:Key="test">
<UserControl.Resources>
<Style x:Key="itemStyle" TargetType="{x:Type ListViewItem}">
<Style.Triggers>
<Trigger Property="ItemsControl.AlternationIndex" Value="0">
<Setter Property="Background" Value="Grey" />
</Trigger>
<Trigger Property="ItemsControl.AlternationIndex" Value="1">
<Setter Property="Background" Value="Yellow" />
</Trigger>
</Style.Triggers>
</Style>
<Style x:Key="itemStyle2" TargetType="{x:Type ListViewItem}">
<Style.Triggers>
<Trigger Property="ItemsControl.AlternationIndex" Value="0">
<Setter Property="Background" Value="Yellow" />
</Trigger>
<Trigger Property="ItemsControl.AlternationIndex" Value="1">
<Setter Property="Background" Value="Grey" />
</Trigger>
</Style.Triggers>
</Style>
</UserControl.Resources>
<ListView AlternationCount="2" ItemContainerStyle="{StaticResource itemStyle}">
<ListView.ItemTemplate>
<DataTemplate>
<ListView AlternationCount="2" ItemContainerStyle="{StaticResource itemStyle2}" />
</DataTemplate>
</ListView.ItemTemplate>
</ListView>
</UserControl>