As for the Bible, I find that the New Testament has a very powerful political spin to it that, without independent corroboration from other writings of the day, makes me very skeptical to accept it as a true and factual historical record. Many of the books attributed to authors contemporary with the time of Christ were actually written after the fact decades later. Further, many of the events, such as the census leading up to Christ's birth in Bethlehem for example, are directly contradicted by Roman governmental records and practices (the Romans never held a census that required everyone to return to the city of their birth).
Granted, most of the works attributed to Paul are indeed likely to have been authored by him, but even they are mainly composed of political letters and communications to colleagues discussing strategy on how to spin Christianity in order to increase its acceptance.
All in all, whereas the Old Testament has a lot of historical verification of at least the general existence and movements of the peoples discussed, the New Testament is much more spurious. It certainly shows signs that it was created after the fact in an effort to vouch for events that the creators of this invented record wanted others to believe really happened.
You sense a deception here? The NIV folks think the four gospels were written some where within 50 to 70 AD. yet they don't see it as a reason to doubt their accuracy. All of the gospels seem to be pretty straight forward about being written after the fact.
As for the works of Josephus, I have not read them. It was just the result of a quick google search to give you a specific non-biblical source.
As for the political spin of the authors of the gospels, they seem to have done pretty well at winning converts in a hostile situation. Those guys must have been brilliant. Its a miracle that the religion they invented was so successful...no wait a minute, not a miracle...just a really good job of spinning. Yeah thats the ticket.