Impossible with default magento setup. You can create configurable product and use simples as black and white options. This will make order view in admin to display selected option sku as ordered product. But you are not able to add additional product as part of that configurable.
You would need to create a module which would add some ability to link those configurable to additional items and then when one of the children is being added/removed from cart you would programmatically add/remove those additional product. If those additional products cannot increase the price you would need either during addition reduce their price to 0 or create cart price rule for that.
For linking products you could use up-sells or cross-sells if you are not using them right now but automatic addition and price management requires some programming work.
Alternatively you could extend bundle product and allow configurable to be part of them. This would require some frontend changes as you would need to somehow load configurable options on bundle product view.
I do not know of any module that can do that, you can search magento marketplace for some solutions.
I just thought of alternative solution within default setup. You can create a bundle product. Your black and white options from configurable add to one group which will allow only for 1 of them to select. The rest of bundled items add to other group or groups depending on your requirements. From backend you should see all skus of simples on the order level.