Use keyup instead of keypress. This gets all the key codes when the user presses something

I came across this myself. I used .on so it looks a bit different but I did this:

 $('#element').on('keypress', function() {
   //code to be executed
 }).on('keydown', function(e) {
   if (e.keyCode==8)
     $('element').trigger('keypress');
 });

Adding my Work Around here. I needed to delete ssn typed by user so i did this in jQuery

  $(this).bind("keydown", function (event) {
        // Allow: backspace, delete
        if (event.keyCode == 46 || event.keyCode == 8) 
        {
            var tempField = $(this).attr('name');
            var hiddenID = tempField.substr(tempField.indexOf('_') + 1);
            $('#' + hiddenID).val('');
            $(this).val('')
            return;
        }  // Allow: tab, escape, and enter
        else if (event.keyCode == 9 || event.keyCode == 27 || event.keyCode == 13 ||
        // Allow: Ctrl+A
        (event.keyCode == 65 && event.ctrlKey === true) ||
        // Allow: home, end, left, right
        (event.keyCode >= 35 && event.keyCode <= 39)) {
            // let it happen, don't do anything
            return;
        }
        else 
        {
            // Ensure that it is a number and stop the keypress
            if (event.shiftKey || (event.keyCode < 48 || event.keyCode > 57) &&       (event.keyCode < 96 || event.keyCode > 105)) 
            {
                event.preventDefault();
            }
        }
    });

If you want to fire the event only on changes of your input use:

$('.s').bind('input', function(){
  console.log("search!");
  doSearch();
});