After trying to find few different ways I ended up using this way, thought might be helpful to others if they are trying to do similar thing.
Instead of passing the value of the elements, I am passing the names of the elements (or id of the element if you want) and in the additional method itself getting the current value of those element using the passed name/id and that worked. .
Below is the updated code:
/*Updated html Form element*/
<input type="checkbox" name="checkBox1" class="{shouldBeEmptyIf: [checkBox1 , dropDownElement]}">
<select name="dropDownElement" size="1" >
<option value="1">One</option>
<option value="2">Two</option>
</select>
/*Updated additional method*/
jQuery.validator.addMethod("shouldBeEmptyIf", function(value, element, param) {
var valid =true;
if($('[name='+ param[0] +']').prop('checked') && $('[name='+ param[1] +']').val()!=''){
valid = false;
}
return valid;
}, "This field must be empty");
Hope this might help.