jQuery.parseJSON() should return an object of type "object", if the string was JSON, so you only have to check the type with typeof
var response=jQuery.parseJSON('response from server');
if(typeof response =='object')
{
// It is JSON
}
else
{
if(response ===false)
{
// the response was a string "false", parseJSON will convert it to boolean false
}
else
{
// the response was something else
}
}