Liberal humanism is a set of beliefs about what is most important in the world. Cultural materialism is a theory about how culture is produced. So cultural materialism would try to explain how liberal humanism has come to dominate our culture today (here in the West).
Liberal humanism is the belief that human beings are the most important things in existence (as opposed to God). People make their own destinies because they are free.
Cultural materialism is influenced by Marx. It says that cultural ideas are produced by the dominant class in a society. It says that the dominant class produces these ideas to help it stay in power. The culture is part of the rulers' way of keeping power.
So cultural materialism would say that liberal humanism is meant to keep the ruling class (capitalists) in power.