$("#getSomethingButton").click(function () {
        var username = "myusername";
        var password = "mypassword";
        $.ajax({
            url: 'people/getSomething',
            username: username,
            password: password,
            dataType: 'jsonp',
            jsonpCallback: 'onGetSomething'
        });
    });

public string GetSomething(string callback)
{
    string data = "{data: 'test'}";
    return string.Format("{0}({1});", callback, data);
}

// Obviously the username/password should not be hardcoded but read from an input
$.get('/home/foo', { username: 'foo', password: 'secret' }, function(result) {
    alert('username/password sent');
});

public ActionResult Foo(string username, string password)
{
    ..
}