The bias in (the non-opinion portions of) major papers like the NYT and WSJ is in what they choose to cover, their depth of coverage, their subtle manipulation of headlines to set the tone of their information, and so on. There is no such thing as selecting what news to report without inherently imbuing it with your bias as to what news is worth knowing.
The best version of this concept is The Week magazine in my opinion (see http://theweek.com/, though I the print version is really higher quality than the site). It includes all the major stories of the week with references and then covers all the columnists and editorials from both sides of the aisle and from around the world. For me, it is the perfect balance of brevity and comprehensiveness without feeling superficial.
AFAIK, it started in the UK and was "ported" to a US edition a few of years ago.
It is pretty easy to read in an hour or so and fills in all the gaps I missed from my sporadic news reading the previous week.
"Much political fanfare was on display at a congressional Finance Committee".... That would be political bias sir, please either don't editorialize, don't publish, or don't claim unbiased.
Yeah, I too am interested in finding out the source of the material along with the claim of it being unbiased. I'm pretty sure that reporting news without bias is impossible.