Equivalent of jQuery .hide() to set visibility: hidden

You could make your own plugins.

jQuery.fn.visible = function() {
    return this.css('visibility', 'visible');
};

jQuery.fn.invisible = function() {
    return this.css('visibility', 'hidden');
};

jQuery.fn.visibilityToggle = function() {
    return this.css('visibility', function(i, visibility) {
        return (visibility == 'visible') ? 'hidden' : 'visible';
    });
};

If you want to overload the original jQuery toggle(), which I don’t recommend…

!(function($) {
    var toggle = $.fn.toggle;
    $.fn.toggle = function() {
        var args = $.makeArray(arguments),
            lastArg = args.pop();

        if (lastArg == 'visibility') {
            return this.visibilityToggle();
        }

        return toggle.apply(this, arguments);
    };
})(jQuery);

jsFiddle.