Well, seeing as the Bible ended centuries before either Jesus or Mohammad was born, nowhere does it mention them by name. But here are some verses why we reject them:
"If a prophet arises among you, or a dreamer of dreams, and gives you a sign or a wonder,and the sign or wonder which he tells you comes to pass, and if he says, `Let us go after other gods,' which you have not known, `and let us serve them,' you shall not listen to the words of that prophet or to that dreamer of dreams; for the LORD your God is testing you, to know whether you love the LORD your God with all your heart and with all your soul. You shall walk after the LORD your God and fear him, and keep his commandments and obey his voice, and you shall serve him and cleave to him."
In addition, neither Jesus nor Mohammad fulfilled the prophecies, and therefore, they cannot be the Messiah.
These prophecies state that
"The moshiach will bring about the political and spiritual redemption of the Jewish people by bringing us back to Israel and restoring Jerusalem (Isaiah 11:11-12; Jeremiah 23:8; 30:3; Hosea 3:4-5). He will establish a government in Israel that will be the center of all world government, both for Jews and gentiles (Isaiah 2:2-4; 11:10; 42:1). He will rebuild the Temple and re-establish its worship (Jeremiah 33:18). He will restore the religious court system of Israel and establish Jewish law as the law of the land (Jeremiah 33:15)."
All traditional Jews hold that Elijah the prophet will return. I don't know if progressive Jews hold this as well.