I have used milk with pretty good results for hyperpigmentation. I like to mix it with orange peel since it really adds a nice fragrance. The smell of milk and hydrogen peroxide mixed together is not appealing to me.
Talking about mixing milk and almond oil together makes me wonder if using something like almond milk or coconut milk would work just as well as regular milk. Using something like this, you might not have to mix it with anything at all.