I'm still tickled when I hear others say that the Buddha is worshipped as a god. He is not worshipped but venerated. To elevate the Buddha to the level of a deity is contrary to Buddhism in the tradition that I practice. But, on to your question. I can appreciate the inner conflict that you must feel with your family being Buddhist and you having embraced Christianity. I face the opposite side of the coin. I have embraced Buddhism but my wife and the majority of my family are Christian. Talk about leaning patience (smile).
The Buddha taught introspection, self analysis, responsibility for one's actions and intention, and a way of life involving meditation to become a better member of society. These same concepts and values found in Buddhism are also inherent in every extant religion. Buddhism may be viewed in two ways: as a purely secular method of right-living that anyone may follow or as a "religious belief" system and structure. A person may read the teachings of the Buddha, find them to be of value and inspiration, and not consider him- / herself to be a Buddhist. Many contemporary theologians of various religious traditions have found pertinent ideas in the Buddha's teachings. But, as the Dalai Lama stated, "Don't try to use what you learn from Buddhism to be a Buddhist; use it to be a better whatever-you-already-are."
Find comfort in your Christian belief. It is good and right for you. I celebrate the peace and comfort that you find in it. Is it possible to be both Christian and Buddhist? Personally, I think it would be problematic. While there are similarities, there are also deep differences. Again, to quote one with greater knowledge than I possess: "...for the Christian practitioner, the Creator and the acceptance of the Creator as almighty, is a very important factor within that tradition in order to develop self-discipline, compassion, or forgiveness and to increase them in one's intimate relationship with God. That's something very essential. In addition, when God is seen as absolute and almighty, the concept that everything is relative becomes a little bit difficult. However, if one's understanding of God is in terms of an ultimate nature of reality or ultimate truth, then it is possible to have a kind of unified approach. ...As to one's personal religion, I think this must be based on one's own mental disposition.... Generally speaking, I think it is better to practice according to your own traditional background, and certainly you can use some of the Buddhist techniques. Without accepting rebirth theory or the complicated philosophy, simply use certain techniques to increase your power of patience and compassion, forgiveness, and things like that." (from "Healing Anger: The Power of Patience from a Buddhist Perspective" by H.H. the Dalai Lama, translated by Thupten Jinpa)
May all be at peace.
John