jQuery - Check if values of inputs, textareas and select not blank in same function

I have the following code which checks if the values of inputs, textareas and selects are blank, but rather than making functions for each I've tried to store them all into one variable using an array.

But, when the click handler is activated, something is causing the error message to appear even when all inputs on the page are filled in.

Anyone know what might be causing this?

HTML:

$('#saveInvoice').click(function(e) {
  e.preventDefault();
  var $fields = [ $('input'), $('textarea'), $('select') ];
  var $emptyFields = $fields.filter(function() {
    return $.trim(this.value) === "";
  });
  if (!$emptyFields.length) {
    saveInvoice();
  } else {
    alert('Unable to save invoice. There are incomplete item fields.');
  }
});