Is Prophet Muhammed (PBUH) part of the family of Ibrahim (PBUH)?

One of my Christian friend and I were discussing about Islam and Christianity. I am not well versed with Prophets and their history. He told me that in the Bible, it is said that the descendants of Ismail (PBUH), first son of Ibrahim (PBUH), will become a great generation and will deviate from the truth. Hence he believes, we are following a different version of Christianity as per the Bible. He did not tell me the bible verse. May be it is part of the new testament. But I initially thought, Muhammed (PBUH) was not related by blood with other prophets. I did some research and tumbled on this . There are lots of comments there. Some say it is false. Some say it is true. Can any scholar shed some light on this matter?