I have a similar issue, but my listview is the 2nd view on a page that is dynamically created, so I want to do this with jquery. I tried this:
$('#tasklist-listview li:nth-child(odd)').addClass('myaltclass');
But the class was applied to all li's. I ran just $('#tasklist-listview li:nth-child(odd)') in the chrome console, and it appeared to return just the alternate li's. Below is the code I use to create the listview.
$("#tasklist-listview").kendoMobileListView({
dataSource: dataSource,
template: kendo.template($("#listviewtemplate").text()),
headerTemplate: "<h3>#:value#</h3>",
filterable: {
field: "Regarding",
operator: "startswith"
}
});