try it by Using java script & hidden field for doing this.
Take hidden field in design.
@Html.Hidden("HdIsPrivate",0)
//Checkbox control
@Html.CheckBox("ChkPrivate", new { @onclick = "CheckIsPrivate()" }) Private
Set hidden field value using javascript.
<script type="text/javascript">
function CheckIsPrivate() {
var x = $("#ChkPrivate").is(":checked");
if (x.toString() == "true") {
document.getElementById('HdIsPrivate').value = '1';
}
else if (x.toString() == "false") {
document.getElementById('HdIsPrivate').value = '0';
}
}
</script>
Access hidden field value in controller.
int is_private = Convert.ToInt32(collection["HdIsPrivate"]);