I know how to serialize the whole form like in example below or one specific field of the form by just changing the line:
data: $(\'form\').serialize(),
Way 1: By comma separated selector you can serialize two fields together using following code
var seializedTwoFields = $('#input-field1,#input-field2').serialize();
Way 2: When you use the jQuery serialize() function, it simply turns your field into a string in the format a=1. So you can certainly apply this function to two fields and concatenate the result, with an & between them.
Please try this snippet.
var formfield1 = $('#input-field1').serialize();
var formfield2 = $('#input-field2').serialize();
var seializedTwoFields = formfield1+'&'+formfield2;